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085A-LowDiscrepancy.f


C PART I:  HALTON SEQUENCE
C PART II: SOBOL SEQUENCE


C ##############################################################################
C PART I: HALTON SEQUENCE:


C This library is free software; you can redistribute it and/or
C modify it under the terms of the GNU Library General Public
C License as published by the Free Software Foundation; either
C version 2 of the License, or (at your option) any later version.
C
C This library is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
C GNU Library General Public License for more details.
C
C You should have received a copy of the GNU Library General 
C Public License along with this library; if not, write to the 
C Free Foundation, Inc., 59 Temple Place, Suite 330, Boston, 
C MA  02111-1307  USA


COPYRIGHT: DIETHELM WUERTZ, SEPT. 2002


C-------------------------------------------------------------------------------

C     INITHALTON (DIMEN, QUASI, BASE, OFFSET)
C     NEXTHALTON (DIMEN, QUASI, BASE, OFFSET)
C     HALTON (QN, N, DIMEN, QUASI, BASE, OFFSET, INIT, TRANSFORM)
C     REAL*8 FUNCTION HQNORM(P)

C-------------------------------------------------------------------------------


      SUBROUTINE INITHALTON(DIMEN, QUASI, BASE, OFFSET)

C     INITIALIZE THE HALTON LOW DISCREPANCY SEQUENCE.
C     THE BASE IS CALCULATED FROM PRIMES

      INTEGER DIMEN, BASE(DIMEN), ITER(DIMEN), OFFSET, DIGIT
      REAL*8 QUASI(DIMEN), HALF
      INTRINSIC MOD
 
C     INIT BASE FROM PRIMES - THIS IMPLEMENTS A SIMMPLE SIEVE:
      BASE(1) = 2
      BASE(2) = 3
      N = 3
      NC = 2
      DO WHILE(NC.LT.DIMEN)
      M = N/2
      K = 0
      IF (MOD(N,2).NE.0.AND.MOD(N,3).NE.0) THEN
         DO I = 5, M
               IF(MOD(N,I).EQ.0) K = K + 1
         ENDDO
         IF (K.EQ.0) THEN
            NC = NC + 1
            BASE(NC) = N
         ENDIF
      ENDIF
      N = N + 1
      ENDDO
      
C     NOW CREATE THE FIRST QUASI RANDOM NUMBER:
      OFFSET = 0
      DO NB = 1, DIMEN        
      ITER(NB) = OFFSET
      QUASI(NB) = 0.0D0
      HALF = 1.0D0 / BASE(NB)
      DO WHILE (ITER(NB).NE.0)
         DIGIT = MOD ( ITER(NB), BASE(NB) )
         QUASI(NB) = QUASI(NB) + DIGIT * HALF
         ITER(NB) = ( ITER(NB) - DIGIT ) / BASE(NB)
         HALF = HALF / BASE(NB)
      ENDDO 
      ENDDO

C     SET THE COUNTER:
      OFFSET = OFFSET + 1
      
      RETURN
      END
  

C-------------------------------------------------------------------------------

  
      SUBROUTINE NEXTHALTON(DIMEN, QUASI, BASE, OFFSET) 

C     GENERATE THE NEXT POINT IN HALTON'S LOW DISCREPANCY SEQUENCE
C     NOTE, THAT WE HAVE ALREADY "OFFSET" POINTS GENERATED.

      INTEGER DIMEN, BASE(DIMEN), ITER(DIMEN), OFFSET, DIGIT
      REAL*8 QUASI(DIMEN), HALF
      INTRINSIC MOD
           
      DO NB = 1, DIMEN      
      ITER(NB) = OFFSET
      QUASI(NB) = 0.0D0
      HALF = 1.0 / BASE(NB)
      DO WHILE (ITER(NB).NE.0)
         DIGIT = MOD ( ITER(NB), BASE(NB) )
         QUASI(NB) = QUASI(NB) + DIGIT * HALF
         ITER(NB) = ( ITER(NB) - DIGIT ) / BASE(NB)
         HALF = HALF / BASE(NB)
      ENDDO 
      ENDDO       

C     INCREASE THE COUNTER BY ONE:
      OFFSET = OFFSET + 1    

      RETURN
      END


C-------------------------------------------------------------------------------   


      SUBROUTINE HALTON(QN, N, DIMEN, BASE, OFFSET, INIT, TRANSFORM)

C     THIS IS AN INTERFACE TO CREATE "N" POINTS IN "DIMEN" DIMENSIONS
C     ARGUMENTS:
C       QN        - THE QUASI NUMBERS, A "N" BY "DIMEN" ARRAY
C       N         - NUMBERS OF POINTS TO GENERATE
C       DIMEN     - THE DIMENSION
C       QUASI     - THE LAST POINT IN THE SEQUENDE
C       BASE      - THE PRIME BASE, A VECTOR OF LENGTH "DIMEN"
C       OFFSET    - THE OFFSET OF POINTS IN THE NEXT FUNCTION CALL
C       INIT      - IF ONE, WE INITIALIZE
C       TRANSFORM - A FLAG, 0 FOR UNIFORM, 1 FOR NORMAL DISTRIBUTION

      INTEGER N, DIMEN, OFFSET, INIT, TRANSFORM
      INTEGER BASE(DIMEN)
      REAL*8 QN(N,DIMEN), QUASI(DIMEN)

C     IF REQUESTED, INITIALIZE THE GENERATOR:
      IF (INIT.EQ.1) THEN
      CALL INITHALTON(DIMEN, QUASI, BASE, OFFSET)    
      ENDIF

C     GENERATE THE NEXT "N" QUASI RANDOM NUMBERS:
      DO I=1, N
         CALL NEXTHALTON(DIMEN, QUASI, BASE, OFFSET)
      IF (TRANSFORM.EQ.1) THEN
         DO J = 1, DIMEN
            QN(I, J) = HQNORM(QUASI(J))
         ENDDO
      ELSE
         DO J = 1, DIMEN
            QN(I, J) = QUASI(J)        
         ENDDO
      ENDIF
      ENDDO

      RETURN
      END


C ------------------------------------------------------------------------------


      REAL*8 FUNCTION HQNORM(P)

C     USED TO CALCULATE HALTON NORMAL DEVIATES:
      REAL*8 P,R,T,A,B, EPS
      DATA P0,P1,P2,P3,P4, Q0,Q1,Q2,Q3,Q4
     &   /-0.322232431088E+0, -1.000000000000E+0, -0.342242088547E+0, 
     &    -0.204231210245E-1, -0.453642210148E-4, +0.993484626060E-1,
     &    +0.588581570495E+0, +0.531103462366E+0, +0.103537752850E+0,  
     &    +0.385607006340E-2  /

C     NOTE, IF P BECOMES 1, THE PROGRAM FAILS TO CALCULATE THE
C     NORMAL RDV. IN THIS CASE WE REPLACE THE LOW DISCREPANCY 
C     POINT WITH A POINT FAR IN THE TAILS.
      EPS = 1.0D-6
      IF (P.GE.(1.0D0-EPS)) P = 1.0d0 - EPS
      IF (P.LE.EPS) P = EPS
      IF (P.NE.0.5D0) GOTO 150
      HQNORM = 0.0D0
      RETURN
150   R = P 
      IF (P.GT.0.5D0) R = 1.0 - R
      T = DSQRT(-2.0*DLOG(R))
      A = ((((T*P4 + P3)*T+P2)*T + P1)*T + P0)
      B = ((((T*Q4 + Q3)*T+Q2)*T + Q1)*T + Q0)
      HQNORM = T + (A/B)
      IF (P.LT.0.5D0) HQNORM = -HQNORM
      
      RETURN
      END 


C -----------------------------------------------------------------------------


      SUBROUTINE TESTHALTON()
      
      INTEGER N1,N2,DIMEN,OFFSET,TRANSFORM
      PARAMETER (N1=20,N2=N1/2,DIMEN=5)
      INTEGER BASE(DIMEN)
      REAL*8 QN1(N1,DIMEN),QN2(N2,DIMEN)

      TRANSFORM = 0
      
C     FIRST TEST RUN:
      INIT = 1
      OFFSET = 0
      CALL HALTON(QN1,N1,DIMEN,BASE,OFFSET,INIT,TRANSFORM)

      WRITE (*,*) 
      WRITE (*,*) "HALTON SEQUENCE: 1-20"  
      WRITE (*,*) 
      WRITE (*,7) "N/DIMEN:", (J, J=1,DIMEN,INT(DIMEN/5))   
      DO I=1, N1, INT(N1/(2*10))
         WRITE (*,8) I, (QN1(I,J), J=1, DIMEN, INT(DIMEN/5))
      ENDDO

C     SECOND TEST RUN:
      INIT=1
      OFFSET = 0
      CALL HALTON(QN2,N2,DIMEN,BASE,OFFSET,INIT,TRANSFORM)
      WRITE (*,*) 
      WRITE (*,*) "HALTON SEQUENCE: 1-10 RE-INITIALIZED"  
      WRITE (*,*)  
      WRITE (*,7) "N/DIMEN:", (J, J=1,DIMEN,INT(DIMEN/5))   
      DO I=1, N2, INT(N2/10)
         WRITE (*,8) I, (QN2(I,J), J=1, DIMEN, INT(DIMEN/5))
      ENDDO

      INIT = 0
      CALL HALTON(QN2,N2,DIMEN,BASE,OFFSET,INIT,TRANSFORM)
      WRITE (*,*) 
      WRITE (*,*) "HALTON SEQUENCE: 11-20 CONTINUED"  
      WRITE (*,*) 
      WRITE (*,7) "N/DIMEN:", (J, J=1,DIMEN,INT(DIMEN/5))   
      DO I=1, N2, INT(N2/10)
         WRITE (*,8) I+N2, (QN2(I,J), J=1, DIMEN, INT(DIMEN/5))
      ENDDO

 7    FORMAT(1H ,A8, 10I10)
 8    FORMAT(1H ,I8, 10F10.6)
      
      RETURN
      END


C ------------------------------------------------------------------------------


c      program mainhalton
c      call testhalton
c      end
  

C ##############################################################################
C PART II: SOBOL SEQUENCE:


COPYRIGHTS:

C     ORIGINAL VERSION:
C       ALGORITHM 659, COLLECTED ALGORITHMS FROM ACM. PUBLISHED IN
C       TRANSACTIONS ON MATHEMATICAL SOFTWARE, VOL. 14, NO. 1, P.88.
C     ADDED SCRAMBLING:
C       FROM PROGRAM "SSOBOL.F" PUBLISHED ON THE INTERNET SITE
C       www.mcqmc.org/Software.html
C     EXTENSION TO MAXD=1111:
C       BY S. JOE ON 17 MAY 2001, SEE:
C     MODIFICATIONS FOR R / SPLUS:
C       BY D. WUERTZ, SEPT. 2002; NOTE THE CHECK OF A VALID DIMENSION
C       VALUE AND THE MAXIMUM NUMBER OF CALLS (ATMOST) HAS TO BE DONE
C       R/SPLUS FUNCTION.
C     SEE:
C       http://www.acm.org/pubs/copyright_policy/softwareCRnotice.html
C
C-------------------------------------------------------------------------------

C     FUNCTIONS:
C       SOBOL (QN, N, DIMEN, QUASI, 
C           LL, COUNT, SV, 
C           IFLAG, iSEED, INIT, TRANSFORM)
C         REAL*8 FUNCTION SQNORM (P)
C       INITSOBOL (DIMEN, QUASI, LL, COUNT, SV, IFLAG, iSEED)
C         SGENSCRML (MAX, LSM, SHIFT, S, MAXCOL, iSEED)
C         SGENSCRMU (USM, USHIFT, S, MAXCOL, iSEED)
C           REAL*8 FUNCTION UNIS (iSEED)
C       NEXTSOBOL (DIMEN, QUASI, LL, COUNT, SV)

C-------------------------------------------------------------------------------


      SUBROUTINE SOBOL(QN, N, DIMEN, QUASI, LL, COUNT, SV,
     &   IFLAG, iSEED, INIT, TRANSFORM)

C     THIS IS AN INTERFACE TO CREATE "N" POINTS IN "DIMEN" DIMENSIONS
C     ARGUMENTS:
C       QN        - QUASI NUMBERS, A "N" BY "DIMEN" ARRAY
C       N         - NUMBERS OF POINTS TO GENERATE
C       DIMEN     - DIMENSION OF THE SEQUENCY
C       QUASI     - LAST POINT IN THE SEQUENDE
C       LL        - COMMON DENOMINATOR OF THE ELEMENTS IN SV
C       COUNT     - SEQUENCE NUMBER OF THE CALL
C       SV        - TABLE OF DIRECTION NUMBERS
C       IFLAG     - INITIALIZATION FLAG
C                   0 - NO SCRAMBLING
C                   1 - OWEN TYPE SCRAMBLING
C                   2 - FAURE-TEZUKA TYPE SCRAMBLING
C                   3 - OWEN + FAURE-TEZUKA TYPE SCRAMBLING
C       iSEED     - SCRAMBLING iSEED
C       INIT      - INITIALIZAYION FLAG, 0 NEXT, 1 RE-INITIALZE
C       TRANSFORM - FLAG, 0 FOR UNIFORM, 1 FOR NORMAL DISTRIBUTION

      INTEGER MAXBIT,N,DIMEN,INIT,TRANSFORM
      PARAMETER (MAXBIT=30)
      INTEGER LL,COUNT,SV(DIMEN,MAXBIT)
      REAL*8 QN(N,DIMEN), QUASI(DIMEN)
      INTEGER iSEED

      IF (INIT.EQ.1) THEN
      CALL INITSOBOL(DIMEN, QUASI, LL, COUNT, SV, IFLAG, iSEED)  
      ENDIF

      DO I=1, N
         CALL NEXTSOBOL(DIMEN, QUASI, LL, COUNT, SV)
      IF (TRANSFORM.EQ.1) THEN
        DO J = 1, DIMEN
               QN(I, J) = SQNORM(QUASI(J))
        ENDDO
      ELSE
            DO J = 1, DIMEN
               QN(I, J) = QUASI(J)         
        ENDDO
      ENDIF
      ENDDO

      RETURN
      END


C ------------------------------------------------------------------------------


      REAL*8 FUNCTION SQNORM(P)

C     USED TO CALCULATE SOBOL NORMAL DEVIATES
      REAL*8 P,R,T,A,B, EPS
      DATA P0,P1,P2,P3,P4, Q0,Q1,Q2,Q3,Q4
     &   /-0.322232431088E+0, -1.000000000000E+0, -0.342242088547E+0, 
     &    -0.204231210245E-1, -0.453642210148E-4, +0.993484626060E-1,
     &    +0.588581570495E+0, +0.531103462366E+0, +0.103537752850E+0,  
     &    +0.385607006340E-2  /

C     NOTE, IF P BECOMES 1, THE PROGRAM FAILS TO CALCULATE THE
C     NORMAL RDV. IN THIS CASE WE REPLACE THE LOW DISCREPANCY 
C     POINT WITH A POINT FAR IN THE TAILS.
      EPS = 1.0D-6
      IF (P.GE.(1.0D0-EPS)) P=1.0D0-EPS
      IF (P.LE.EPS) P=EPS
      IF (P.NE.0.5D0) GOTO 150
      SQNORM = 0.0D0
      RETURN
150   R = P 
      IF (P.GT.0.5D0) R = 1.0 - R
      T = DSQRT(-2.0*DLOG(R))
      A = ((((T*P4 + P3)*T+P2)*T + P1)*T + P0)
      B = ((((T*Q4 + Q3)*T+Q2)*T + Q1)*T + Q0)
      SQNORM = T + (A/B)
      IF (P.LT.0.5D0) SQNORM = -SQNORM
     
      RETURN
      END 


C ------------------------------------------------------------------------------

     
      SUBROUTINE INITSOBOL(DIMEN, QUASI, LL, COUNT, SV, 
     &   IFLAG, iSEED)

C     INITIALIZATION OF THE SOBOL GENERATOR:
C       THE LEADING ELEMENTS OF EACH ROW OF SV ARE INITIALIZED USING "VINIT".
C         EACH ROW CORRESPONDS TO A PRIMITIVE POLYNOMIAL. IF THE POLYNOMIAL 
C         HAS DEGREE "M", ELEMENTS AFTER THE FIRST "M" ARE CALCULATED.
C       THE NUMBERS IN "SV" ARE ACTUALLY BINARY FRACTIONS. "RECIPD=1/LL"  
C         HOLDS 1/(THE COMMON DENOMINATOR OF ALL OF THEM).
C       INITSOBOL IMPLICITLY COMPUTES THE FIRST ALL-ZERO VECTOR.
C       THE TAUS" IS FOR DETERMINING "FAVORABLE" VALUES. AS DISCUSSED IN 
C         BRATLEY/FOX, HESE HAVE THE FORM "N=2**K" WHERE "K.GE.(TAUS+S-1)"
C         FOR INTEGRATION AND "K.GT.TAUS" FOR GLOBAL OPTIMIZATION.
C     ARGUMENTS:
C       DIMEN     - DIMENSION OF THE SEQUENCY
C       QUASI     - LAST POINT IN THE SEQUENDE
C       LL        - COMMON DENOMINATOR OF THE ELEMENTS IN SV
C       COUNT     - SEQUENCE NUMBER OF THE CALL
C       SV        - TABLE OF DIRECTION NUMBERS
C       IFLAG     - INITIALIZATION FLAG
C                   0 - NO SCRAMBLING
C                   1 - OWEN TYPE SCRAMBLING
C                   2 - FAURE-TEZUKA TYPE SCRAMBLING
C                   3 - OWEN + FAURE-TEZUKA TYPE SCRAMBLING
C       iSEED     - SCRAMBLING iSEED
      
      INTEGER MAXDIM,MAXDEG,MAXBIT,IFLAG
CC      DW ADDED FOLLOWING LINE:
      INTEGER P,PP
      PARAMETER (MAXDIM=1111,MAXDEG=13,MAXBIT=30)
      INTEGER ATMOST,DIMEN,TAUS,COUNT,MAXCOL,S
      INTEGER POLY(2:MAXDIM),VINIT(2:MAXDIM,MAXDEG)
      INTEGER SV(DIMEN,MAXBIT),V(DIMEN,MAXBIT)
      INTEGER I,J,K,L,M,NEWV,TAU(MAXDEG)
      INTEGER USM(31,31),USHIFT(31)
CC      INTEGER TEMP1,TEMP2,TEMP4
      INTEGER TEMP1,TEMP2,TEMP3,TEMP4
      INTEGER SHIFT(1111),LSM(1111,31),TV(1111,31,31)
      REAL*8 QUASI(DIMEN),RECIPD
      INTEGER iSEED
      LOGICAL INCLUD(MAXDEG)
      INTRINSIC MOD, IEOR
      
      DATA (POLY(I),I=2,211)/3,7,11,13,19,25,37,59,47,61,55,41,67,97,91,
     +     109,103,115,131,193,137,145,143,241,157,185,167,229,171,213,
     +     191,253,203,211,239,247,285,369,299,301,333,351,355,357,361,
     +     391,397,425,451,463,487,501,529,539,545,557,563,601,607,617,
     +     623,631,637,647,661,675,677,687,695,701,719,721,731,757,761,
     +     787,789,799,803,817,827,847,859,865,875,877,883,895,901,911,
     +     949,953,967,971,973,981,985,995,1001,1019,1033,1051,1063,
     +     1069,1125,1135,1153,1163,1221,1239,1255,1267,1279,1293,1305,
     +     1315,1329,1341,1347,1367,1387,1413,1423,1431,1441,1479,1509,
     +     1527,1531,1555,1557,1573,1591,1603,1615,1627,1657,1663,1673,
     +     1717,1729,1747,1759,1789,1815,1821,1825,1849,1863,1869,1877,
     +     1881,1891,1917,1933,1939,1969,2011,2035,2041,2053,2071,2091,
     +     2093,2119,2147,2149,2161,2171,2189,2197,2207,2217,2225,2255,
     +     2257,2273,2279,2283,2293,2317,2323,2341,2345,2363,2365,2373,
     +     2377,2385,2395,2419,2421,2431,2435,2447,2475,2477,2489,2503,
     +     2521,2533,2551,2561,2567,2579,2581,2601,2633,2657,2669/
      DATA (POLY(I),I=212,401)/2681,2687,2693,2705,2717,2727,2731,2739,
     +     2741,2773,2783,2793,2799,2801,2811,2819,2825,2833,2867,2879,
     +     2881,2891,2905,2911,2917,2927,2941,2951,2955,2963,2965,2991,
     +     2999,3005,3017,3035,3037,3047,3053,3083,3085,3097,3103,3159,
     +     3169,3179,3187,3205,3209,3223,3227,3229,3251,3263,3271,3277,
     +     3283,3285,3299,3305,3319,3331,3343,3357,3367,3373,3393,3399,
     +     3413,3417,3427,3439,3441,3475,3487,3497,3515,3517,3529,3543,
     +     3547,3553,3559,3573,3589,3613,3617,3623,3627,3635,3641,3655,
     +     3659,3669,3679,3697,3707,3709,3713,3731,3743,3747,3771,3791,
     +     3805,3827,3833,3851,3865,3889,3895,3933,3947,3949,3957,3971,
     +     3985,3991,3995,4007,4013,4021,4045,4051,4069,4073,4179,4201,
     +     4219,4221,4249,4305,4331,4359,4383,4387,4411,4431,4439,4449,
     +     4459,4485,4531,4569,4575,4621,4663,4669,4711,4723,4735,4793,
     +     4801,4811,4879,4893,4897,4921,4927,4941,4977,5017,5027,5033,
     +     5127,5169,5175,5199,5213,5223,5237,5287,5293,5331,5391,5405,
     +     5453,5523,5573,5591,5597,5611,5641,5703,5717,5721,5797,5821,
     +     5909,5913/
      DATA (POLY(I),I=402,591)/5955,5957,6005,6025,6061,6067,6079,6081,
     +     6231,6237,6289,6295,6329,6383,6427,6453,6465,6501,6523,6539,
     +     6577,6589,6601,6607,6631,6683,6699,6707,6761,6795,6865,6881,
     +     6901,6923,6931,6943,6999,7057,7079,7103,7105,7123,7173,7185,
     +     7191,7207,7245,7303,7327,7333,7355,7365,7369,7375,7411,7431,
     +     7459,7491,7505,7515,7541,7557,7561,7701,7705,7727,7749,7761,
     +     7783,7795,7823,7907,7953,7963,7975,8049,8089,8123,8125,8137,
     +     8219,8231,8245,8275,8293,8303,8331,8333,8351,8357,8367,8379,
     +     8381,8387,8393,8417,8435,8461,8469,8489,8495,8507,8515,8551,
     +     8555,8569,8585,8599,8605,8639,8641,8647,8653,8671,8675,8689,
     +     8699,8729,8741,8759,8765,8771,8795,8797,8825,8831,8841,8855,
     +     8859,8883,8895,8909,8943,8951,8955,8965,8999,9003,9031,9045,
     +     9049,9071,9073,9085,9095,9101,9109,9123,9129,9137,9143,9147,
     +     9185,9197,9209,9227,9235,9247,9253,9257,9277,9297,9303,9313,
     +     9325,9343,9347,9371,9373,9397,9407,9409,9415,9419,9443,9481,
     +     9495,9501,9505,9517,9529,9555,9557,9571,9585,9591,9607,9611,
     +     9621,9625/
      DATA (POLY(I),I=592,765)/9631,9647,9661,9669,9679,9687,9707,9731,
     +     9733,9745,9773,9791,9803,9811,9817,9833,9847,9851,9863,9875,
     +     9881,9905,9911,9917,9923,9963,9973,10003,10025,10043,10063,
     +     10071,10077,10091,10099,10105,10115,10129,10145,10169,10183,
     +     10187,10207,10223,10225,10247,10265,10271,10275,10289,10299,
     +     10301,10309,10343,10357,10373,10411,10413,10431,10445,10453,
     +     10463,10467,10473,10491,10505,10511,10513,10523,10539,10549,
     +     10559,10561,10571,10581,10615,10621,10625,10643,10655,10671,
     +     10679,10685,10691,10711,10739,10741,10755,10767,10781,10785,
     +     10803,10805,10829,10857,10863,10865,10875,10877,10917,10921,
     +     10929,10949,10967,10971,10987,10995,11009,11029,11043,11045,
     +     11055,11063,11075,11081,11117,11135,11141,11159,11163,11181,
     +     11187,11225,11237,11261,11279,11297,11307,11309,11327,11329,
     +     11341,11377,11403,11405,11413,11427,11439,11453,11461,11473,
     +     11479,11489,11495,11499,11533,11545,11561,11567,11575,11579,
     +     11589,11611,11623,11637,11657,11663,11687,11691,11701,11747,
     +     11761,11773,11783,11795,11797,11817,11849,11855,11867,11869,
     +     11873,11883,11919/
      DATA (POLY(I),I=766,936)/11921,11927,11933,11947,11955,11961,
     +     11999,12027,12029,12037,12041,12049,12055,12095,12097,12107,
     +     12109,12121,12127,12133,12137,12181,12197,12207,12209,12239,
     +     12253,12263,12269,12277,12287,12295,12309,12313,12335,12361,
     +     12367,12391,12409,12415,12433,12449,12469,12479,12481,12499,
     +     12505,12517,12527,12549,12559,12597,12615,12621,12639,12643,
     +     12657,12667,12707,12713,12727,12741,12745,12763,12769,12779,
     +     12781,12787,12799,12809,12815,12829,12839,12857,12875,12883,
     +     12889,12901,12929,12947,12953,12959,12969,12983,12987,12995,
     +     13015,13019,13031,13063,13077,13103,13137,13149,13173,13207,
     +     13211,13227,13241,13249,13255,13269,13283,13285,13303,13307,
     +     13321,13339,13351,13377,13389,13407,13417,13431,13435,13447,
     +     13459,13465,13477,13501,13513,13531,13543,13561,13581,13599,
     +     13605,13617,13623,13637,13647,13661,13677,13683,13695,13725,
     +     13729,13753,13773,13781,13785,13795,13801,13807,13825,13835,
     +     13855,13861,13871,13883,13897,13905,13915,13939,13941,13969,
     +     13979,13981,13997,14027,14035,14037,14051,14063,14085,14095,
     +     14107,14113,14125,14137,14145/
      DATA (POLY(I),I=937,1107)/14151,14163,14193,14199,14219,14229,
     +     14233,14243,14277,14287,14289,14295,14301,14305,14323,14339,
     +     14341,14359,14365,14375,14387,14411,14425,14441,14449,14499,
     +     14513,14523,14537,14543,14561,14579,14585,14593,14599,14603,
     +     14611,14641,14671,14695,14701,14723,14725,14743,14753,14759,
     +     14765,14795,14797,14803,14831,14839,14845,14855,14889,14895,
     +     14909,14929,14941,14945,14951,14963,14965,14985,15033,15039,
     +     15053,15059,15061,15071,15077,15081,15099,15121,15147,15149,
     +     15157,15167,15187,15193,15203,15205,15215,15217,15223,15243,
     +     15257,15269,15273,15287,15291,15313,15335,15347,15359,15373,
     +     15379,15381,15391,15395,15397,15419,15439,15453,15469,15491,
     +     15503,15517,15527,15531,15545,15559,15593,15611,15613,15619,
     +     15639,15643,15649,15661,15667,15669,15681,15693,15717,15721,
     +     15741,15745,15765,15793,15799,15811,15825,15835,15847,15851,
     +     15865,15877,15881,15887,15899,15915,15935,15937,15955,15973,
     +     15977,16011,16035,16061,16069,16087,16093,16097,16121,16141,
     +     16153,16159,16165,16183,16189,16195,16197,16201,16209,16215,
     +     16225,16259,16265,16273,16299/
      DATA (POLY(I),I=1108,1111)/16309,16355,16375,16381/
      
      DATA (VINIT(I,1),I=2,1111)/1110*1/
      DATA (VINIT(I,2),I=3,401)/1,3,1,3,1,3,3,1,3,1,3,1,3,1,1,3,1,3,1,3,
     +     1,3,3,1,1,1,3,1,3,1,3,3,1,3,1,1,1,3,1,3,1,1,1,3,3,1,3,3,1,1,
     +     3,3,1,3,3,3,1,3,1,3,1,1,3,3,1,1,1,1,3,1,1,3,1,1,1,3,3,1,3,3,
     +     1,3,3,3,1,3,3,3,1,3,3,1,3,3,3,1,3,1,3,1,1,3,3,1,3,3,1,1,1,3,
     +     3,1,3,3,1,3,1,1,3,3,3,1,1,1,3,1,1,3,1,1,3,3,1,3,1,3,3,3,3,1,
     +     1,1,3,3,1,1,3,1,1,1,1,1,1,3,1,3,1,1,1,3,1,3,1,3,3,3,1,1,3,3,
     +     1,3,1,3,1,1,3,1,3,1,3,1,3,1,1,1,3,3,1,3,3,1,3,1,1,1,3,1,3,1,
     +     1,3,1,1,3,3,1,1,3,3,3,1,3,3,3,1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,
     +     1,1,3,3,3,1,1,1,1,3,3,3,1,3,3,1,1,1,1,3,1,1,3,1,3,3,1,1,3,3,
     +     1,1,1,1,3,1,3,3,1,3,3,1,1,1,3,3,3,1,3,3,1,3,3,1,3,1,3,3,3,1,
     +     3,1,1,3,1,3,1,1,1,3,3,3,1,1,3,1,3,1,1,1,1,1,1,3,1,1,3,1,3,3,
     +     1,1,1,1,3,1,3,1,3,1,1,1,1,3,3,1,1,1,1,1,3,3,3,1,1,3,3,3,3,3,
     +     1,3,3,1,3,3,3,3,1,1,1,1,1,1,3,1,1,3,1,1,1,3,1,1,1,3,3,3,1,3,
     +     1,1,3,3,3,1,3,3,1,3,1,3,3,1,3,3,3,1,1/
      DATA (VINIT(I,2),I=402,800)/3,3,1,3,1,3,1,1,1,3,3,3,3,1,3,1,1,3,1,
     +     3,1,1,1,3,1,3,1,3,1,3,3,3,3,3,3,3,3,1,3,3,3,3,3,1,3,1,3,3,3,
     +     1,3,1,3,1,3,3,1,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,3,3,1,1,3,3,1,
     +     1,1,3,3,1,1,3,3,3,3,1,1,3,1,3,3,1,3,3,1,1,1,3,3,3,1,1,3,3,3,
     +     3,3,1,1,1,3,1,3,3,1,3,3,3,3,1,1,3,1,1,3,1,3,1,3,1,3,3,1,1,3,
     +     3,1,3,3,1,3,3,1,1,3,1,3,3,1,1,3,1,3,1,3,1,1,3,3,1,1,1,3,3,1,
     +     3,1,1,3,3,1,1,3,1,3,1,1,1,1,1,3,1,1,1,1,3,1,3,1,1,3,3,1,1,3,
     +     1,3,1,3,3,3,1,3,3,3,1,1,3,3,3,1,1,1,1,3,1,3,1,3,1,1,3,3,1,1,
     +     1,3,3,1,3,1,3,1,1,1,1,1,1,3,1,3,3,1,3,3,3,1,3,1,1,3,3,1,1,3,
     +     3,1,1,1,3,1,3,3,1,1,3,1,1,3,1,3,1,1,1,3,3,3,3,1,1,3,3,1,1,1,
     +     1,3,1,1,3,3,3,1,1,3,3,1,3,3,1,1,3,3,3,3,3,3,3,1,3,3,1,3,1,3,
     +     1,1,3,3,1,1,1,3,1,3,3,1,3,3,1,3,1,1,3,3,3,1,1,1,3,1,1,1,3,3,
     +     3,1,3,3,1,3,1,1,3,3,3,1,3,3,1,1,1,3,1,3,3,3,3,3,3,3,3,1,3,3,
     +     1,3,1,1,3,3,3,1,3,3,3,3,3,1,3,3,3,1,1,1/
      DATA (VINIT(I,2),I=801,1111)/3,3,1,3,3,1,3,1,3,1,3,1,3,3,3,3,3,3,
     +     1,1,3,1,3,1,1,1,1,1,3,1,1,1,3,1,3,1,1,3,3,3,1,3,1,3,1,1,3,1,
     +     3,3,1,3,1,3,3,1,3,3,1,3,3,3,3,3,3,1,3,1,1,3,3,3,1,1,3,3,3,3,
     +     3,3,3,1,3,3,3,3,1,3,1,3,3,3,1,3,1,3,1,1,1,3,3,1,3,1,1,3,3,1,
     +     3,1,1,1,1,3,1,3,1,1,3,1,3,1,3,3,3,3,3,3,1,3,3,3,3,1,3,3,1,3,
     +     3,3,3,3,1,1,1,1,3,3,3,1,3,3,1,1,3,3,1,1,3,3,1,3,1,1,3,1,3,3,
     +     3,3,3,1,3,1,1,3,3,3,3,1,3,1,1,3,3,3,3,3,3,1,1,3,1,3,1,1,3,1,
     +     1,1,1,3,3,1,1,3,1,1,1,3,1,3,1,1,3,3,1,3,1,1,3,3,3,3,3,1,3,1,
     +     1,1,3,1,1,1,3,1,1,3,1,3,3,3,3,3,1,1,1,3,3,3,3,1,3,3,3,3,1,1,
     +     3,3,3,1,3,1,1,3,3,1,3,3,1,1,1,1,1,3,1,1,3,3,1,1,1,3,1,1,3,3,
     +     1,3,3,3,3,3,3,3,3,1,1,3,3,1,1,3,1,3,3,3,3,3,1/
      DATA (VINIT(I,3),I=4,402)/7,5,1,3,3,7,5,5,7,7,1,3,3,7,5,1,1,5,3,7,
     +     1,7,5,1,3,7,7,1,1,1,5,7,7,5,1,3,3,7,5,5,5,3,3,3,1,1,5,1,1,5,
     +     3,3,3,3,1,3,7,5,7,3,7,1,3,3,5,1,3,5,5,7,7,7,1,1,3,3,1,1,5,1,
     +     5,7,5,1,7,5,3,3,1,5,7,1,7,5,1,7,3,1,7,1,7,3,3,5,7,3,3,5,1,3,
     +     3,1,3,5,1,3,3,3,7,1,1,7,3,1,3,7,5,5,7,5,5,3,1,3,3,3,1,3,3,7,
     +     3,3,1,7,5,1,7,7,5,7,5,1,3,1,7,3,7,3,5,7,3,1,3,3,3,1,5,7,3,3,
     +     7,7,7,5,3,1,7,1,3,7,5,3,3,3,7,1,1,3,1,5,7,1,3,5,3,5,3,3,7,5,
     +     5,3,3,1,3,7,7,7,1,5,7,1,3,1,1,7,1,3,1,7,1,5,3,5,3,1,1,5,5,3,
     +     3,5,7,1,5,3,7,7,3,5,3,3,1,7,3,1,3,5,7,1,3,7,1,5,1,3,1,5,3,1,
     +     7,1,5,5,5,3,7,1,1,7,3,1,1,7,5,7,5,7,7,3,7,1,3,7,7,3,5,1,1,7,
     +     1,5,5,5,1,5,1,7,5,5,7,1,1,7,1,7,7,1,1,3,3,3,7,7,5,3,7,3,1,3,
     +     7,5,3,3,5,7,1,1,5,5,7,7,1,1,1,1,5,5,5,7,5,7,1,1,3,5,1,3,3,7,
     +     3,7,5,3,5,3,1,7,1,7,7,1,1,7,7,7,5,5,1,1,7,5,5,7,5,1,1,5,5,5,
     +     5,5,5,1,3,1,5,7,3,3,5,7,3,7,1,7,7,1,3/
      DATA (VINIT(I,3),I=403,801)/5,1,5,5,3,7,3,7,7,5,7,5,7,1,1,5,3,5,1,
     +     5,3,7,1,5,7,7,3,5,1,3,5,1,5,3,3,3,7,3,5,1,3,7,7,3,7,5,3,3,1,
     +     7,5,1,1,3,7,1,7,1,7,3,7,3,5,7,3,5,3,1,1,1,5,7,7,3,3,1,1,1,5,
     +     5,7,3,1,1,3,3,7,3,3,5,1,3,7,3,3,7,3,5,7,5,7,7,3,3,5,1,3,5,3,
     +     1,3,5,1,1,3,7,7,1,5,1,3,7,3,7,3,5,1,7,1,1,3,5,3,7,1,5,5,1,1,
     +     3,1,3,3,7,1,7,3,1,7,3,1,7,3,5,3,5,7,3,3,3,5,1,7,7,1,3,1,3,7,
     +     7,1,3,7,3,1,5,3,1,1,1,5,3,3,7,1,5,3,5,1,3,1,3,1,5,7,7,1,1,5,
     +     3,1,5,1,1,7,7,3,5,5,1,7,1,5,1,1,3,1,5,7,5,7,7,1,5,1,1,3,5,1,
     +     5,5,3,1,3,1,5,5,3,3,3,3,1,1,3,1,3,5,5,7,5,5,7,5,7,1,3,7,7,3,
     +     5,5,7,5,5,3,3,3,1,7,1,5,5,5,3,3,5,1,3,1,3,3,3,7,1,7,7,3,7,1,
     +     1,5,7,1,7,1,7,7,1,3,7,5,1,3,5,5,5,1,1,7,1,7,1,7,7,3,1,1,5,1,
     +     5,1,5,3,5,5,5,5,5,3,3,7,3,3,5,5,3,7,1,5,7,5,1,5,5,3,5,5,7,5,
     +     3,5,5,5,1,5,5,5,5,1,3,5,3,1,7,5,5,7,1,5,3,3,1,5,3,7,1,7,5,1,
     +     1,3,1,1,7,1,5,5,3,7,3,7,5,3,1,1,3,1,3,5/
      DATA (VINIT(I,3),I=802,1111)/5,7,5,3,7,7,7,3,7,3,7,1,3,1,7,7,1,7,
     +     3,7,3,7,3,7,3,5,1,1,7,3,1,5,5,7,1,5,5,5,7,1,5,5,1,5,5,3,1,3,
     +     1,7,3,1,3,5,7,7,7,1,1,7,3,1,5,5,5,1,1,1,1,1,5,3,5,1,3,5,3,1,
     +     1,1,1,3,7,3,7,5,7,1,5,5,7,5,3,3,7,5,3,1,1,3,1,3,1,1,3,7,1,7,
     +     1,1,5,1,7,5,3,7,3,5,3,1,1,5,5,1,7,7,3,7,3,7,1,5,1,5,3,7,3,5,
     +     7,7,7,3,3,1,1,5,5,3,7,1,1,1,3,5,3,1,1,3,3,7,5,1,1,3,7,1,5,7,
     +     3,7,5,5,7,3,5,3,1,5,3,1,1,7,5,1,7,3,7,5,1,7,1,7,7,1,1,7,1,5,
     +     5,1,1,7,5,7,1,5,3,5,3,3,7,1,5,1,1,5,5,3,3,7,5,5,1,1,1,3,1,5,
     +     7,7,1,7,5,7,3,7,3,1,3,7,3,1,5,5,3,5,1,3,5,5,5,1,1,7,7,1,5,5,
     +     1,3,5,1,5,3,5,3,3,7,5,7,3,7,3,1,3,7,7,3,3,1,1,3,3,3,3,3,5,5,
     +     3,3,3,1,3,5,7,7,1,5,7,3,7,1,1,3,5,7,5,3,3,3/
      DATA (VINIT(I,4),I=6,357)/1,7,9,13,11,1,3,7,9,5,13,13,11,3,15,5,3,
     +     15,7,9,13,9,1,11,7,5,15,1,15,11,5,11,1,7,9,7,7,1,15,15,15,13,
     +     3,3,15,5,9,7,13,3,7,5,11,9,1,9,1,5,7,13,9,9,1,7,3,5,1,11,11,
     +     13,7,7,9,9,1,1,3,9,15,1,5,13,1,9,9,9,9,9,13,11,3,5,11,11,13,
     +     5,3,15,1,11,11,7,13,15,11,13,9,11,15,15,13,3,15,7,9,11,13,11,
     +     9,9,5,13,9,1,13,7,7,7,7,7,5,9,7,13,11,9,11,15,3,13,11,1,11,3,
     +     3,9,11,1,7,1,15,15,3,1,9,1,7,13,11,3,13,11,7,3,3,5,13,11,5,
     +     11,1,3,9,7,15,7,5,13,7,9,13,15,13,9,7,15,7,9,5,11,11,13,13,9,
     +     3,5,13,9,11,15,11,7,1,7,13,3,13,3,13,9,15,7,13,13,3,13,15,15,
     +     11,9,13,9,15,1,1,15,11,11,7,1,11,13,9,13,3,5,11,13,9,9,13,1,
     +     11,15,13,3,13,7,15,1,15,3,3,11,7,13,7,7,9,7,5,15,9,5,5,7,15,
     +     13,15,5,15,5,3,1,11,7,1,5,7,9,3,11,1,15,1,3,15,11,13,5,13,1,
     +     7,1,15,7,5,1,1,15,13,11,11,13,5,11,7,9,7,1,5,3,9,5,5,11,5,1,
     +     7,1,11,7,9,13,15,13,3,1,11,13,15,1,1,11,9,13,3,13,11,15,13,9,
     +     9,9,5,5,5,5,1,15,5,9/
      DATA (VINIT(I,4),I=358,710)/11,7,15,5,3,13,5,3,11,5,1,11,13,9,11,
     +     3,7,13,15,1,7,11,1,13,1,15,1,9,7,3,9,11,1,9,13,13,3,11,7,9,1,
     +     7,15,9,1,5,13,5,11,3,9,15,11,13,5,1,7,7,5,13,7,7,9,5,11,11,1,
     +     1,15,3,13,9,13,9,9,11,5,5,13,15,3,9,15,3,11,11,15,15,3,11,15,
     +     15,3,1,3,1,3,3,1,3,13,1,11,5,15,7,15,9,1,7,1,9,11,15,1,13,9,
     +     13,11,7,3,7,3,13,7,9,7,7,3,3,9,9,7,5,11,13,13,7,7,15,9,5,5,3,
     +     3,13,3,9,3,1,11,1,3,11,15,11,11,11,9,13,7,9,15,9,11,1,3,3,9,
     +     7,15,13,13,7,15,9,13,9,15,13,15,9,13,1,11,7,11,3,13,5,1,7,15,
     +     3,13,7,13,13,11,3,5,3,13,11,9,9,3,11,11,7,9,13,11,7,15,13,7,
     +     5,3,1,5,15,15,3,11,1,7,3,15,11,5,5,3,5,5,1,15,5,1,5,3,7,5,11,
     +     3,13,9,13,15,5,3,5,9,5,3,11,1,13,9,15,3,5,11,9,1,3,15,9,9,9,
     +     11,7,5,13,1,15,3,13,9,13,5,1,5,1,13,13,7,7,1,9,5,11,9,11,13,
     +     3,15,15,13,15,7,5,7,9,7,9,9,9,11,9,3,11,15,13,13,5,9,15,1,1,
     +     9,5,13,3,13,15,3,1,3,11,13,1,15,9,9,3,1,9,1,9,1,13,11,15,7,
     +     11,15,13,15,1,9,9,7/
      DATA (VINIT(I,4),I=711,1065)/3,5,11,7,3,9,5,15,7,5,3,13,7,1,1,9,
     +     15,15,15,11,3,5,15,13,7,15,15,11,11,9,5,15,9,7,3,13,1,1,5,1,
     +     3,1,7,1,1,5,1,11,11,9,9,5,13,7,7,7,1,1,9,9,11,11,15,7,5,5,3,
     +     11,1,3,7,13,7,7,7,3,15,15,11,9,3,9,3,15,13,5,3,3,3,5,9,15,9,
     +     9,1,5,9,9,15,5,15,7,9,1,9,9,5,11,5,15,15,11,7,7,7,1,1,11,11,
     +     13,15,3,13,5,1,7,1,11,3,13,15,3,5,3,5,7,3,9,9,5,1,7,11,9,3,5,
     +     11,13,13,13,9,15,5,7,1,15,11,9,15,15,13,13,13,1,11,9,15,9,5,
     +     15,5,7,3,11,3,15,7,13,11,7,3,7,13,5,13,15,5,13,9,1,15,11,5,5,
     +     1,11,3,3,7,1,9,7,15,9,9,3,11,15,7,1,3,1,1,1,9,1,5,15,15,7,5,
     +     5,7,9,7,15,13,13,11,1,9,11,1,13,1,7,15,15,5,5,1,11,3,9,11,9,
     +     9,9,1,9,3,5,15,1,1,9,7,3,3,1,9,9,11,9,9,13,13,3,13,11,13,5,1,
     +     5,5,9,9,3,13,13,9,15,9,11,7,11,9,13,9,1,15,9,7,7,1,7,9,9,15,
     +     1,11,1,13,13,15,9,13,7,15,3,9,3,1,13,7,5,9,3,1,7,1,1,13,3,3,
     +     11,1,7,13,15,15,5,7,13,13,15,11,13,1,13,13,3,9,15,15,11,15,9,
     +     15,1,13,15,1,1,5/
      DATA (VINIT(I,4),I=1066,1111)/11,5,1,11,11,5,3,9,1,3,5,13,9,7,7,1,
     +     9,9,15,7,5,5,15,13,9,7,13,3,13,11,13,7,9,13,13,13,15,9,5,5,3,
     +     3,3,1,3,15/
      DATA (VINIT(I,5),I=8,331)/9,3,27,15,29,21,23,19,11,25,7,13,17,1,
     +     25,29,3,31,11,5,23,27,19,21,5,1,17,13,7,15,9,31,25,3,5,23,7,
     +     3,17,23,3,3,21,25,25,23,11,19,3,11,31,7,9,5,17,23,17,17,25,
     +     13,11,31,27,19,17,23,7,5,11,19,19,7,13,21,21,7,9,11,1,5,21,
     +     11,13,25,9,7,7,27,15,25,15,21,17,19,19,21,5,11,3,5,29,31,29,
     +     5,5,1,31,27,11,13,1,3,7,11,7,3,23,13,31,17,1,27,11,25,1,23,
     +     29,17,25,7,25,27,17,13,17,23,5,17,5,13,11,21,5,11,5,9,31,19,
     +     17,9,9,27,21,15,15,1,1,29,5,31,11,17,23,19,21,25,15,11,5,5,1,
     +     19,19,19,7,13,21,17,17,25,23,19,23,15,13,5,19,25,9,7,3,21,17,
     +     25,1,27,25,27,25,9,13,3,17,25,23,9,25,9,13,17,17,3,15,7,7,29,
     +     3,19,29,29,19,29,13,15,25,27,1,3,9,9,13,31,29,31,5,15,29,1,
     +     19,5,9,19,5,15,3,5,7,15,17,17,23,11,9,23,19,3,17,1,27,9,9,17,
     +     13,25,29,23,29,11,31,25,21,29,19,27,31,3,5,3,3,13,21,9,29,3,
     +     17,11,11,9,21,19,7,17,31,25,1,27,5,15,27,29,29,29,25,27,25,3,
     +     21,17,25,13,15,17,13,23,9,3,11,7,9,9,7,17,7,1/
      DATA (VINIT(I,5),I=332,654)/27,1,9,5,31,21,25,25,21,11,1,23,19,27,
     +     15,3,5,23,9,25,7,29,11,9,13,5,11,1,3,31,27,3,17,27,11,13,15,
     +     29,15,1,15,23,25,13,21,15,3,29,29,5,25,17,11,7,15,5,21,7,31,
     +     13,11,23,5,7,23,27,21,29,15,7,27,27,19,7,15,27,27,19,19,9,15,
     +     1,3,29,29,5,27,31,9,1,7,3,19,19,29,9,3,21,31,29,25,1,3,9,27,
     +     5,27,25,21,11,29,31,27,21,29,17,9,17,13,11,25,15,21,11,19,31,
     +     3,19,5,3,3,9,13,13,3,29,7,5,9,23,13,21,23,21,31,11,7,7,3,23,
     +     1,23,5,9,17,21,1,17,29,7,5,17,13,25,17,9,19,9,5,7,21,19,13,9,
     +     7,3,9,3,15,31,29,29,25,13,9,21,9,31,7,15,5,31,7,15,27,25,19,
     +     9,9,25,25,23,1,9,7,11,15,19,15,27,17,11,11,31,13,25,25,9,7,
     +     13,29,19,5,19,31,25,13,25,15,5,9,29,31,9,29,27,25,27,11,17,5,
     +     17,3,23,15,9,9,17,17,31,11,19,25,13,23,15,25,21,31,19,3,11,
     +     25,7,15,19,7,5,3,13,13,1,23,5,25,11,25,15,13,21,11,23,29,5,
     +     17,27,9,19,15,5,29,23,19,1,27,3,23,21,19,27,11,17,13,27,11,
     +     31,23,5,9,21,31,29,11,21,17,15,7,15,7,9,21,27,25/
      DATA (VINIT(I,5),I=655,975)/29,11,3,21,13,23,19,27,17,29,25,17,9,
     +     1,19,23,5,23,1,17,17,13,27,23,7,7,11,13,17,13,11,21,13,23,1,
     +     27,13,9,7,1,27,29,5,13,25,21,3,31,15,13,3,19,13,1,27,15,17,1,
     +     3,13,13,13,31,29,27,7,7,21,29,15,17,17,21,19,17,3,15,5,27,27,
     +     3,31,31,7,21,3,13,11,17,27,25,1,9,7,29,27,21,23,13,25,29,15,
     +     17,29,9,15,3,21,15,17,17,31,9,9,23,19,25,3,1,11,27,29,1,31,
     +     29,25,29,1,23,29,25,13,3,31,25,5,5,11,3,21,9,23,7,11,23,11,1,
     +     1,3,23,25,23,1,23,3,27,9,27,3,23,25,19,29,29,13,27,5,9,29,29,
     +     13,17,3,23,19,7,13,3,19,23,5,29,29,13,13,5,19,5,17,9,11,11,
     +     29,27,23,19,17,25,13,1,13,3,11,1,17,29,1,13,17,9,17,21,1,11,
     +     1,1,25,5,7,29,29,19,19,1,29,13,3,1,31,15,13,3,1,11,19,5,29,
     +     13,29,23,3,1,31,13,19,17,5,5,1,29,23,3,19,25,19,27,9,27,13,
     +     15,29,23,13,25,25,17,19,17,15,27,3,25,17,27,3,27,31,23,13,31,
     +     11,15,7,21,19,27,19,21,29,7,31,13,9,9,7,21,13,11,9,11,29,19,
     +     11,19,21,5,29,13,7,19,19,27,23,31,1,27,21,7,3,7,11/
      DATA (VINIT(I,5),I=976,1111)/23,13,29,11,31,19,1,5,5,11,5,3,27,5,
     +     7,11,31,1,27,31,31,23,5,21,27,9,25,3,15,19,1,19,9,5,25,21,15,
     +     25,29,15,21,11,19,15,3,7,13,11,25,17,1,5,31,13,29,23,9,5,29,
     +     7,17,27,7,17,31,9,31,9,9,7,21,3,3,3,9,11,21,11,31,9,25,5,1,
     +     31,13,29,9,29,1,11,19,7,27,13,31,7,31,7,25,23,21,29,11,11,13,
     +     11,27,1,23,31,21,23,21,19,31,5,31,25,25,19,17,11,25,7,13,1,
     +     29,17,23,15,7,29,17,13,3,17/
      DATA (VINIT(I,6),I=14,324)/37,33,7,5,11,39,63,59,17,15,23,29,3,21,
     +     13,31,25,9,49,33,19,29,11,19,27,15,25,63,55,17,63,49,19,41,
     +     59,3,57,33,49,53,57,57,39,21,7,53,9,55,15,59,19,49,31,3,39,5,
     +     5,41,9,19,9,57,25,1,15,51,11,19,61,53,29,19,11,9,21,19,43,13,
     +     13,41,25,31,9,11,19,5,53,37,7,51,45,7,7,61,23,45,7,59,41,1,
     +     29,61,37,27,47,15,31,35,31,17,51,13,25,45,5,5,33,39,5,47,29,
     +     35,47,63,45,37,47,59,21,59,33,51,9,27,13,25,43,3,17,21,59,61,
     +     27,47,57,11,17,39,1,63,21,59,17,13,31,3,31,7,9,27,37,23,31,9,
     +     45,43,31,63,21,39,51,27,7,53,11,1,59,39,23,49,23,7,55,59,3,
     +     19,35,13,9,13,15,23,9,7,43,55,3,19,9,27,33,27,49,23,47,19,7,
     +     11,55,27,35,5,5,55,35,37,9,33,29,47,25,11,47,53,61,59,3,53,
     +     47,5,19,59,5,47,23,45,53,3,49,61,47,39,29,17,57,5,17,31,23,
     +     41,39,5,27,7,29,29,33,31,41,31,29,17,29,29,9,9,31,27,53,35,5,
     +     61,1,49,13,57,29,5,21,43,25,57,49,37,27,11,61,37,49,5,63,63,
     +     3,45,37,63,21,21,19,27,59,21,45,23,13,15,3,43,63,39,19/
      DATA (VINIT(I,6),I=325,632)/63,31,41,41,15,43,63,53,1,63,31,7,17,
     +     11,61,31,51,37,29,59,25,63,59,47,15,27,19,29,45,35,55,39,19,
     +     43,21,19,13,17,51,37,5,33,35,49,25,45,1,63,47,9,63,15,25,25,
     +     15,41,13,3,19,51,49,37,25,49,13,53,47,23,35,29,33,21,35,23,3,
     +     43,31,63,9,1,61,43,3,11,55,11,35,1,63,35,49,19,45,9,57,51,1,
     +     47,41,9,11,37,19,55,23,55,55,13,7,47,37,11,43,17,3,25,19,55,
     +     59,37,33,43,1,5,21,5,63,49,61,21,51,15,19,43,47,17,9,53,45,
     +     11,51,25,11,25,47,47,1,43,29,17,31,15,59,27,63,11,41,51,29,7,
     +     27,63,31,43,3,29,39,3,59,59,1,53,63,23,63,47,51,23,61,39,47,
     +     21,39,15,3,9,57,61,39,37,21,51,1,23,43,27,25,11,13,21,43,7,
     +     11,33,55,1,37,35,27,61,39,5,19,61,61,57,59,21,59,61,57,25,55,
     +     27,31,41,33,63,19,57,35,13,63,35,17,11,11,49,41,55,5,45,17,
     +     35,5,31,31,37,17,45,51,1,39,49,55,19,41,13,5,51,5,49,1,21,13,
     +     17,59,51,11,3,61,1,33,37,33,61,25,27,59,7,49,13,63,3,33,3,15,
     +     9,13,35,39,11,59,59,1,57,11,5,57,13,31,13,11,55,45,9,55,55/
      DATA (VINIT(I,6),I=633,942)/19,25,41,23,45,29,63,59,27,39,21,37,7,
     +     61,49,35,39,9,29,7,25,23,57,5,19,15,33,49,37,25,17,45,29,15,
     +     25,3,3,49,11,39,15,19,57,39,15,11,3,57,31,55,61,19,5,41,35,
     +     59,61,39,41,53,53,63,31,9,59,13,35,55,41,49,5,41,25,27,43,5,
     +     5,43,5,5,17,5,15,27,29,17,9,3,55,31,1,45,45,13,57,17,3,61,15,
     +     49,15,47,9,37,45,9,51,61,21,33,11,21,63,63,47,57,61,49,9,59,
     +     19,29,21,23,55,23,43,41,57,9,39,27,41,35,61,29,57,63,21,31,
     +     59,35,49,3,49,47,49,33,21,19,21,35,11,17,37,23,59,13,37,35,
     +     55,57,1,29,45,11,1,15,9,33,19,53,43,39,23,7,13,13,1,19,41,55,
     +     1,13,15,59,55,15,3,57,37,31,17,1,3,21,29,25,55,9,37,33,53,41,
     +     51,19,57,13,63,43,19,7,13,37,33,19,15,63,51,11,49,23,57,47,
     +     51,15,53,41,1,15,37,61,11,35,29,33,23,55,11,59,19,61,61,45,
     +     13,49,13,63,5,61,5,31,17,61,63,13,27,57,1,21,5,11,39,57,51,
     +     53,39,25,41,39,37,23,31,25,33,17,57,29,27,23,47,41,29,19,47,
     +     41,25,5,51,43,39,29,7,31,45,51,49,55,17,43,49,45,9,29,3,5,47,
     +     9,15,19/
      DATA (VINIT(I,6),I=943,1111)/51,45,57,63,9,21,59,3,9,13,45,23,15,
     +     31,21,15,51,35,9,11,61,23,53,29,51,45,31,29,5,35,29,53,35,17,
     +     59,55,27,51,59,27,47,15,29,37,7,49,55,5,19,45,29,19,57,33,53,
     +     45,21,9,3,35,29,43,31,39,3,45,1,41,29,5,59,41,33,35,27,19,13,
     +     25,27,43,33,35,17,17,23,7,35,15,61,61,53,5,15,23,11,13,43,55,
     +     47,25,43,15,57,45,1,49,63,57,15,31,31,7,53,27,15,47,23,7,29,
     +     53,47,9,53,3,25,55,45,63,21,17,23,31,27,27,43,63,55,63,45,51,
     +     15,27,5,37,43,11,27,5,27,59,21,7,39,27,63,35,47,55,17,17,17,
     +     3,19,21,13,49,61,39,15/
      DATA (VINIT(I,7),I=20,305)/13,33,115,41,79,17,29,119,75,73,105,7,
     +     59,65,21,3,113,61,89,45,107,21,71,79,19,71,61,41,57,121,87,
     +     119,55,85,121,119,11,23,61,11,35,33,43,107,113,101,29,87,119,
     +     97,29,17,89,5,127,89,119,117,103,105,41,83,25,41,55,69,117,
     +     49,127,29,1,99,53,83,15,31,73,115,35,21,89,5,1,91,53,35,95,
     +     83,19,85,55,51,101,33,41,55,45,95,61,27,37,89,75,57,61,15,
     +     117,15,21,27,25,27,123,39,109,93,51,21,91,109,107,45,15,93,
     +     127,3,53,81,79,107,79,87,35,109,73,35,83,107,1,51,7,59,33,
     +     115,43,111,45,121,105,125,87,101,41,95,75,1,57,117,21,27,67,
     +     29,53,117,63,1,77,89,115,49,127,15,79,81,29,65,103,33,73,79,
     +     29,21,113,31,33,107,95,111,59,99,117,63,63,99,39,9,35,63,125,
     +     99,45,93,33,93,9,105,75,51,115,11,37,17,41,21,43,73,19,93,7,
     +     95,81,93,79,81,55,9,51,63,45,89,73,19,115,39,47,81,39,5,5,45,
     +     53,65,49,17,105,13,107,5,5,19,73,59,43,83,97,115,27,1,69,103,
     +     3,99,103,63,67,25,121,97,77,13,83,103,41,11,27,81,37,33,125,
     +     71,41,41,59,41,87,123/
      DATA (VINIT(I,7),I=306,589)/43,101,63,45,39,21,97,15,97,111,21,49,
     +     13,17,79,91,65,105,75,1,45,67,83,107,125,87,15,81,95,105,65,
     +     45,59,103,23,103,99,67,99,47,117,71,89,35,53,73,9,115,49,37,
     +     1,35,9,45,81,19,127,17,17,105,89,49,101,7,37,33,11,95,95,17,
     +     111,105,41,115,5,69,101,27,27,101,103,53,9,21,43,79,91,65,
     +     117,87,125,55,45,63,85,83,97,45,83,87,113,93,95,5,17,77,77,
     +     127,123,45,81,85,121,119,27,85,41,49,15,107,21,51,119,11,87,
     +     101,115,63,63,37,121,109,7,43,69,19,77,49,71,59,35,7,13,55,
     +     101,127,103,85,109,29,61,67,21,111,67,23,57,75,71,101,123,41,
     +     107,101,107,125,27,47,119,41,19,127,33,31,109,7,91,91,39,125,
     +     105,47,125,123,91,9,103,45,23,117,9,125,73,11,37,61,79,21,5,
     +     47,117,67,53,85,33,81,121,47,61,51,127,29,65,45,41,95,57,73,
     +     33,117,61,111,59,123,65,47,105,23,29,107,37,81,67,29,115,119,
     +     75,73,99,103,7,57,45,61,95,49,101,101,35,47,119,39,67,31,103,
     +     7,61,127,87,3,35,29,73,95,103,71,75,51,87,57,97,11,105,87,41,
     +     73,109,69,35,121,39,111,1,77/
      DATA (VINIT(I,7),I=590,875)/39,47,53,91,3,17,51,83,39,125,85,111,
     +     21,69,85,29,55,11,117,1,47,17,65,63,47,117,17,115,51,25,33,
     +     123,123,83,51,113,95,121,51,91,109,43,55,35,55,87,33,37,5,3,
     +     45,21,105,127,35,17,35,37,97,97,21,77,123,17,89,53,105,75,25,
     +     125,13,47,21,125,23,55,63,61,5,17,93,57,121,69,73,93,121,105,
     +     75,91,67,95,75,9,69,97,99,93,11,53,19,73,5,33,79,107,65,69,
     +     79,125,25,93,55,61,17,117,69,97,87,111,37,93,59,79,95,53,115,
     +     53,85,85,65,59,23,75,21,67,27,99,79,27,3,95,27,69,19,75,47,
     +     59,41,85,77,99,55,49,93,93,119,51,125,63,13,15,45,61,19,105,
     +     115,17,83,7,7,11,61,37,63,89,95,119,113,67,123,91,33,37,99,
     +     43,11,33,65,81,79,81,107,63,63,55,89,91,25,93,101,27,55,75,
     +     121,79,43,125,73,27,109,35,21,71,113,89,59,95,41,45,113,119,
     +     113,39,59,73,15,13,59,67,121,27,7,105,15,59,59,35,91,89,23,
     +     125,97,53,41,91,111,29,31,3,103,61,71,35,7,119,29,45,49,111,
     +     41,109,59,125,13,27,19,79,9,75,83,81,33,91,109,33,29,107,111,
     +     101,107,109,65,59,43,37/
      DATA (VINIT(I,7),I=876,1111)/1,9,15,109,37,111,113,119,79,73,65,
     +     71,93,17,101,87,97,43,23,75,109,41,49,53,31,97,105,109,119,
     +     51,9,53,113,97,73,89,79,49,61,105,13,99,53,71,7,87,21,101,5,
     +     71,31,123,121,121,73,79,115,13,39,101,19,37,51,83,97,55,81,
     +     91,127,105,89,63,47,49,75,37,77,15,49,107,23,23,35,19,69,17,
     +     59,63,73,29,125,61,65,95,101,81,57,69,83,37,11,37,95,1,73,27,
     +     29,57,7,65,83,99,69,19,103,43,95,25,19,103,41,125,97,71,105,
     +     83,83,61,39,9,45,117,63,31,5,117,67,125,41,117,43,77,97,15,
     +     29,5,59,25,63,87,39,39,77,85,37,81,73,89,29,125,109,21,23,
     +     119,105,43,93,97,15,125,29,51,69,37,45,31,75,109,119,53,5,
     +     101,125,121,35,29,7,63,17,63,13,69,15,105,51,127,105,9,57,95,
     +     59,109,35,49,23,33,107,55,33,57,79,73,69,59,107,55,11,63,95,
     +     103,23,125,91,31,91,51,65,61,75,69,107,65,101,59,35,15/
      DATA (VINIT(I,8),I=38,299)/7,23,39,217,141,27,53,181,169,35,15,
     +     207,45,247,185,117,41,81,223,151,81,189,61,95,185,23,73,113,
     +     239,85,9,201,83,53,183,203,91,149,101,13,111,239,3,205,253,
     +     247,121,189,169,179,197,175,217,249,195,95,63,19,7,5,75,217,
     +     245,111,189,165,169,141,221,249,159,253,207,249,219,23,49,
     +     127,237,5,25,177,37,103,65,167,81,87,119,45,79,143,57,79,187,
     +     143,183,75,97,211,149,175,37,135,189,225,241,63,33,43,13,73,
     +     213,57,239,183,117,21,29,115,43,205,223,15,3,159,51,101,127,
     +     99,239,171,113,171,119,189,245,201,27,185,229,105,153,189,33,
     +     35,137,77,97,17,181,55,197,201,155,37,197,137,223,25,179,91,
     +     23,235,53,253,49,181,249,53,173,97,247,67,115,103,159,239,69,
     +     173,217,95,221,247,97,91,123,223,213,129,181,87,239,85,89,
     +     249,141,39,57,249,71,101,159,33,137,189,71,253,205,171,13,
     +     249,109,131,199,189,179,31,99,113,41,173,23,189,197,3,135,9,
     +     95,195,27,183,1,123,73,53,99,197,59,27,101,55,193,31,61,119,
     +     11,7,255,233,53,157,193,97,83,65,81,239,167,69,71,109/
      DATA (VINIT(I,8),I=300,559)/97,137,71,193,189,115,79,205,37,227,
     +     53,33,91,229,245,105,77,229,161,103,93,13,161,229,223,69,15,
     +     25,23,233,93,25,217,247,61,75,27,9,223,213,55,197,145,89,199,
     +     41,201,5,149,35,119,183,53,11,13,3,179,229,43,55,187,233,47,
     +     133,91,47,71,93,105,145,45,255,221,115,175,19,129,5,209,197,
     +     57,177,115,187,119,77,211,111,33,113,23,87,137,41,7,83,43,
     +     121,145,5,219,27,11,111,207,55,97,63,229,53,33,149,23,187,
     +     153,91,193,183,59,211,93,139,59,179,163,209,77,39,111,79,229,
     +     85,237,199,137,147,25,73,121,129,83,87,93,205,167,53,107,229,
     +     213,95,219,109,175,13,209,97,61,147,19,13,123,73,35,141,81,
     +     19,171,255,111,107,233,113,133,89,9,231,95,69,33,1,253,219,
     +     253,247,129,11,251,221,153,35,103,239,7,27,235,181,5,207,53,
     +     149,155,225,165,137,155,201,97,245,203,47,39,35,105,239,49,
     +     15,253,7,237,213,55,87,199,27,175,49,41,229,85,3,149,179,129,
     +     185,249,197,15,97,197,139,203,63,33,251,217,199,199,99,249,
     +     33,229,177,13,209,147,97,31,125,177,137/
      DATA (VINIT(I,8),I=560,819)/187,11,91,223,29,169,231,59,31,163,41,
     +     57,87,247,25,127,101,207,187,73,61,105,27,91,171,243,33,3,1,
     +     21,229,93,71,61,37,183,65,211,53,11,151,165,47,5,129,79,101,
     +     147,169,181,19,95,77,139,197,219,97,239,183,143,9,13,209,23,
     +     215,53,137,203,19,151,171,133,219,231,3,15,253,225,33,111,
     +     183,213,169,119,111,15,201,123,121,225,113,113,225,161,165,1,
     +     139,55,3,93,217,193,97,29,69,231,161,93,69,143,137,9,87,183,
     +     113,183,73,215,137,89,251,163,41,227,145,57,81,57,11,135,145,
     +     161,175,159,25,55,167,157,211,97,247,249,23,129,159,71,197,
     +     127,141,219,5,233,131,217,101,131,33,157,173,69,207,239,81,
     +     205,11,41,169,65,193,77,201,173,1,221,157,1,15,113,147,137,
     +     205,225,73,45,49,149,113,253,99,17,119,105,117,129,243,75,
     +     203,53,29,247,35,247,171,31,199,213,29,251,7,251,187,91,11,
     +     149,13,205,37,249,137,139,9,7,113,183,205,187,39,3,79,155,
     +     227,89,185,51,127,63,83,41,133,183,181,127,19,255,219,59,251,
     +     3,187,57,217,115,217,229,181,185,149,83,115,11/
      DATA (VINIT(I,8),I=820,1074)/123,19,109,165,103,123,219,129,155,
     +     207,177,9,49,181,231,33,233,67,155,41,9,95,123,65,117,249,85,
     +     169,129,241,173,251,225,147,165,69,81,239,95,23,83,227,249,
     +     143,171,193,9,21,57,73,97,57,29,239,151,159,191,47,51,1,223,
     +     251,251,151,41,119,127,131,33,209,123,53,241,25,31,183,107,
     +     25,115,39,11,213,239,219,109,185,35,133,123,185,27,55,245,61,
     +     75,205,213,169,163,63,55,49,83,195,51,31,41,15,203,41,63,127,
     +     161,5,143,7,199,251,95,75,101,15,43,237,197,117,167,155,21,
     +     83,205,255,49,101,213,237,135,135,21,73,93,115,7,85,223,237,
     +     79,89,5,57,239,67,65,201,155,71,85,195,89,181,119,135,147,
     +     237,173,41,155,67,113,111,21,183,23,103,207,253,69,219,205,
     +     195,43,197,229,139,177,129,69,97,201,163,189,11,99,91,253,
     +     239,91,145,19,179,231,121,7,225,237,125,191,119,59,175,237,
     +     131,79,43,45,205,199,251,153,207,37,179,113,255,107,217,61,7,
     +     181,247,31,13,113,145,107,233,233,43,79,23,169,137,129,183,
     +     53,91,55,103,223,87,177,157,79,213,139/
      DATA (VINIT(I,8),I=1075,1111)/183,231,205,143,129,243,205,93,59,
     +     15,89,9,11,47,133,227,75,9,91,19,171,163,79,7,103,5,119,155,
     +     75,11,71,95,17,13,243,207,187/
      DATA (VINIT(I,9),I=54,299)/235,307,495,417,57,151,19,119,375,451,
     +     55,449,501,53,185,317,17,21,487,13,347,393,15,391,307,189,
     +     381,71,163,99,467,167,433,337,257,179,47,385,23,117,369,425,
     +     207,433,301,147,333,85,221,423,49,3,43,229,227,201,383,281,
     +     229,207,21,343,251,397,173,507,421,443,399,53,345,77,385,317,
     +     155,187,269,501,19,169,235,415,61,247,183,5,257,401,451,95,
     +     455,49,489,75,459,377,87,463,155,233,115,429,211,419,143,487,
     +     195,209,461,193,157,193,363,181,271,445,381,231,135,327,403,
     +     171,197,181,343,113,313,393,311,415,267,247,425,233,289,55,
     +     39,247,327,141,5,189,183,27,337,341,327,87,429,357,265,251,
     +     437,201,29,339,257,377,17,53,327,47,375,393,369,403,125,429,
     +     257,157,217,85,267,117,337,447,219,501,41,41,193,509,131,207,
     +     505,421,149,111,177,167,223,291,91,29,305,151,177,337,183,
     +     361,435,307,507,77,181,507,315,145,423,71,103,493,271,469,
     +     339,237,437,483,31,219,61,131,391,233,219,69,57,459,225,421,
     +     7,461,111,451,277,185,193,125,251,199,73,71,7,409,417,149/
      DATA (VINIT(I,9),I=300,550)/193,53,437,29,467,229,31,35,75,105,
     +     503,75,317,401,367,131,365,441,433,93,377,405,465,259,283,
     +     443,143,445,3,461,329,309,77,323,155,347,45,381,315,463,207,
     +     321,157,109,479,313,345,167,439,307,235,473,79,101,245,19,
     +     381,251,35,25,107,187,115,113,321,115,445,61,77,293,405,13,
     +     53,17,171,299,41,79,3,485,331,13,257,59,201,497,81,451,199,
     +     171,81,253,365,75,451,149,483,81,453,469,485,305,163,401,15,
     +     91,3,129,35,239,355,211,387,101,299,67,375,405,357,267,363,
     +     79,83,437,457,39,97,473,289,179,57,23,49,79,71,341,287,95,
     +     229,271,475,49,241,261,495,353,381,13,291,37,251,105,399,81,
     +     89,265,507,205,145,331,129,119,503,249,1,289,463,163,443,63,
     +     123,361,261,49,429,137,355,175,507,59,277,391,25,185,381,197,
     +     39,5,429,119,247,177,329,465,421,271,467,151,45,429,137,471,
     +     11,17,409,347,199,463,177,11,51,361,95,497,163,351,127,395,
     +     511,327,353,49,105,151,321,331,329,509,107,109,303,467,287,
     +     161,45,385,289,363,331,265,407,37,433,315,343,63,51,185,71,
     +     27,267/
      DATA (VINIT(I,9),I=551,798)/503,239,293,245,281,297,75,461,371,
     +     129,189,189,339,287,111,111,379,93,27,185,347,337,247,507,
     +     161,231,43,499,73,327,263,331,249,493,37,25,115,3,167,197,
     +     127,357,497,103,125,191,165,55,101,95,79,351,341,43,125,135,
     +     173,289,373,133,421,241,281,213,177,363,151,227,145,363,239,
     +     431,81,397,241,67,291,255,405,421,399,75,399,105,329,41,425,
     +     7,283,375,475,427,277,209,411,3,137,195,289,509,121,55,147,
     +     275,251,19,129,285,415,487,491,193,219,403,23,97,65,285,75,
     +     21,373,261,339,239,495,415,333,107,435,297,213,149,463,199,
     +     323,45,19,301,121,499,187,229,63,425,99,281,35,125,349,87,
     +     101,59,195,511,355,73,263,243,101,165,141,11,389,219,187,449,
     +     447,393,477,305,221,51,355,209,499,479,265,377,145,411,173,
     +     11,433,483,135,385,341,89,209,391,33,395,319,451,119,341,227,
     +     375,61,331,493,411,293,47,203,375,167,395,155,5,237,361,489,
     +     127,21,345,101,371,233,431,109,119,277,125,263,73,135,123,83,
     +     123,405,69,75,287,401,23,283,393,41,379,431,11,475,505,19,
     +     365,265,271/
      DATA (VINIT(I,9),I=799,1045)/499,489,443,165,91,83,291,319,199,
     +     107,245,389,143,137,89,125,281,381,215,131,299,249,375,455,
     +     43,73,281,217,297,229,431,357,81,357,171,451,481,13,387,491,
     +     489,439,385,487,177,393,33,71,375,443,129,407,395,127,65,333,
     +     309,119,197,435,497,373,71,379,509,387,159,265,477,463,449,
     +     47,353,249,335,505,89,141,55,235,187,87,363,93,363,101,67,
     +     215,321,331,305,261,411,491,479,65,307,469,415,131,315,487,
     +     83,455,19,113,163,503,99,499,251,239,81,167,391,255,317,363,
     +     359,395,419,307,251,267,171,461,183,465,165,163,293,477,223,
     +     403,389,97,335,357,297,19,469,501,249,85,213,311,265,379,297,
     +     283,393,449,463,289,159,289,499,407,129,137,221,43,89,403,
     +     271,75,83,445,453,389,149,143,423,499,317,445,157,137,453,
     +     163,87,23,391,119,427,323,173,89,259,377,511,249,31,363,229,
     +     353,329,493,427,57,205,389,91,83,13,219,439,45,35,371,441,17,
     +     267,501,53,25,333,17,201,475,257,417,345,381,377,55,403,77,
     +     389,347,363,211,413,419,5,167,219,201,285,425,11,77,269,489,
     +     281,403,79/
      DATA (VINIT(I,9),I=1046,1111)/425,125,81,331,437,271,397,299,475,
     +     271,249,413,233,261,495,171,69,27,409,21,421,367,81,483,255,
     +     15,219,365,497,181,75,431,99,325,407,229,281,63,83,493,5,113,
     +     15,271,37,87,451,299,83,451,311,441,47,455,47,253,13,109,369,
     +     347,11,409,275,63,441,15/
      DATA (VINIT(I,10),I=102,344)/519,307,931,1023,517,771,151,1023,
     +     539,725,45,927,707,29,125,371,275,279,817,389,453,989,1015,
     +     29,169,743,99,923,981,181,693,309,227,111,219,897,377,425,
     +     609,227,19,221,143,581,147,919,127,725,793,289,411,835,921,
     +     957,443,349,813,5,105,457,393,539,101,197,697,27,343,515,69,
     +     485,383,855,693,133,87,743,747,475,87,469,763,721,345,479,
     +     965,527,121,271,353,467,177,245,627,113,357,7,691,725,355,
     +     889,635,737,429,545,925,357,873,187,351,677,999,921,477,233,
     +     765,495,81,953,479,89,173,473,131,961,411,291,967,65,511,13,
     +     805,945,369,827,295,163,835,259,207,331,29,315,999,133,967,
     +     41,117,677,471,717,881,755,351,723,259,879,455,721,289,149,
     +     199,805,987,851,423,597,129,11,733,549,153,285,451,559,377,
     +     109,357,143,693,615,677,701,475,767,85,229,509,547,151,389,
     +     711,785,657,319,509,99,1007,775,359,697,677,85,497,105,615,
     +     891,71,449,835,609,377,693,665,627,215,911,503,729,131,19,
     +     895,199,161,239,633,1013,537,255,23,149,679,1021,595,199,557,
     +     659,251,829,727,439,495,647,223/
      DATA (VINIT(I,10),I=345,586)/949,625,87,481,85,799,917,769,949,
     +     739,115,499,945,547,225,1015,469,737,495,353,103,17,665,639,
     +     525,75,447,185,43,729,577,863,735,317,99,17,477,893,537,519,
     +     1017,375,297,325,999,353,343,729,135,489,859,267,141,831,141,
     +     893,249,807,53,613,131,547,977,131,999,175,31,341,739,467,
     +     675,241,645,247,391,583,183,973,433,367,131,467,571,309,385,
     +     977,111,917,935,473,345,411,313,97,149,959,841,839,669,431,
     +     51,41,301,247,1015,377,329,945,269,67,979,581,643,823,557,91,
     +     405,117,801,509,347,893,303,227,783,555,867,99,703,111,797,
     +     873,541,919,513,343,319,517,135,871,917,285,663,301,15,763,
     +     89,323,757,317,807,309,1013,345,499,279,711,915,411,281,193,
     +     739,365,315,375,809,469,487,621,857,975,537,939,585,129,625,
     +     447,129,1017,133,83,3,415,661,53,115,903,49,79,55,385,261,
     +     345,297,199,385,617,25,515,275,849,401,471,377,661,535,505,
     +     939,465,225,929,219,955,659,441,117,527,427,515,287,191,33,
     +     389,197,825,63,417,949,35,571,9,131,609,439,95,19,569,893,
     +     451,397,971,801/
      DATA (VINIT(I,10),I=587,824)/125,471,187,257,67,949,621,453,411,
     +     621,955,309,783,893,597,377,753,145,637,941,593,317,555,375,
     +     575,175,403,571,555,109,377,931,499,649,653,329,279,271,647,
     +     721,665,429,957,803,767,425,477,995,105,495,575,687,385,227,
     +     923,563,723,481,717,111,633,113,369,955,253,321,409,909,367,
     +     33,967,453,863,449,539,781,911,113,7,219,725,1015,971,1021,
     +     525,785,873,191,893,297,507,215,21,153,645,913,755,371,881,
     +     113,903,225,49,587,201,927,429,599,513,97,319,331,833,325,
     +     887,139,927,399,163,307,803,169,1019,869,537,907,479,335,697,
     +     479,353,769,787,1023,855,493,883,521,735,297,1011,991,879,
     +     855,591,415,917,375,453,553,189,841,339,211,601,57,765,745,
     +     621,209,875,639,7,595,971,263,1009,201,23,77,621,33,535,963,
     +     661,523,263,917,103,623,231,47,301,549,337,675,189,357,1005,
     +     789,189,319,721,1005,525,675,539,191,813,917,51,167,415,579,
     +     755,605,721,837,529,31,327,799,961,279,409,847,649,241,285,
     +     545,407,161,591,73,313,811,17,663,269,261,37,783,127,917,231,
     +     577,975,793/
      DATA (VINIT(I,10),I=825,1065)/921,343,751,139,221,79,817,393,545,
     +     11,781,71,1,699,767,917,9,107,341,587,903,965,599,507,843,
     +     739,579,397,397,325,775,565,925,75,55,979,931,93,957,857,753,
     +     965,795,67,5,87,909,97,995,271,875,671,613,33,351,69,811,669,
     +     729,401,647,241,435,447,721,271,745,53,775,99,343,451,427,
     +     593,339,845,243,345,17,573,421,517,971,499,435,769,75,203,
     +     793,985,343,955,735,523,659,703,303,421,951,405,631,825,735,
     +     433,841,485,49,749,107,669,211,497,143,99,57,277,969,107,397,
     +     563,551,447,381,187,57,405,731,769,923,955,915,737,595,341,
     +     253,823,197,321,315,181,885,497,159,571,981,899,785,947,217,
     +     217,135,753,623,565,717,903,581,955,621,361,869,87,943,907,
     +     853,353,335,197,771,433,743,195,91,1023,63,301,647,205,485,
     +     927,1003,987,359,577,147,141,1017,701,273,89,589,487,859,343,
     +     91,847,341,173,287,1003,289,639,983,685,697,35,701,645,911,
     +     501,705,873,763,745,657,559,699,315,347,429,197,165,955,859,
     +     167,303,833,531,473,635,641,195,589,821,205,3,635,371,891,
     +     249,123/
      DATA (VINIT(I,10),I=1066,1111)/77,623,993,401,525,427,71,655,951,
     +     357,851,899,535,493,323,1003,343,515,859,1017,5,423,315,1011,
     +     703,41,777,163,95,831,79,975,235,633,723,297,589,317,679,981,
     +     195,399,1003,121,501,155/
      DATA (VINIT(I,11),I=162,376)/7,2011,1001,49,825,415,1441,383,1581,
     +     623,1621,1319,1387,619,839,217,75,1955,505,281,1629,1379,53,
     +     1111,1399,301,209,49,155,1647,631,129,1569,335,67,1955,1611,
     +     2021,1305,121,37,877,835,1457,669,1405,935,1735,665,551,789,
     +     1543,1267,1027,1,1911,163,1929,67,1975,1681,1413,191,1711,
     +     1307,401,725,1229,1403,1609,2035,917,921,1789,41,2003,187,67,
     +     1635,717,1449,277,1903,1179,363,1211,1231,647,1261,1029,1485,
     +     1309,1149,317,1335,171,243,271,1055,1601,1129,1653,205,1463,
     +     1681,1621,197,951,573,1697,1265,1321,1805,1235,1853,1307,945,
     +     1197,1411,833,273,1517,1747,1095,1345,869,57,1383,221,1713,
     +     335,1751,1141,839,523,1861,1105,389,1177,1877,805,93,1591,
     +     423,1835,99,1781,1515,1909,1011,303,385,1635,357,973,1781,
     +     1707,1363,1053,649,1469,623,1429,1241,1151,1055,503,921,3,
     +     349,1149,293,45,303,877,1565,1583,1001,663,1535,395,1141,
     +     1481,1797,643,1507,465,2027,1695,367,937,719,545,1991,83,819,
     +     239,1791,1461,1647,1501,1161,1629,139,1595,1921,1267,1415,
     +     509,347,777,1083,363,269,1015/
      DATA (VINIT(I,11),I=377,589)/1809,1105,1429,1471,2019,381,2025,
     +     1223,827,1733,887,1321,803,1951,1297,1995,833,1107,1135,1181,
     +     1251,983,1389,1565,273,137,71,735,1005,933,67,1471,551,457,
     +     1667,1729,919,285,1629,1815,653,1919,1039,531,393,1411,359,
     +     221,699,1485,471,1357,1715,595,1677,153,1903,1281,215,781,
     +     543,293,1807,965,1695,443,1985,321,879,1227,1915,839,1945,
     +     1993,1165,51,557,723,1491,817,1237,947,1215,1911,1225,1965,
     +     1889,1503,1177,73,1767,303,177,1897,1401,321,921,217,1779,
     +     327,1889,333,615,1665,1825,1639,237,1205,361,129,1655,983,
     +     1089,1171,401,677,643,749,303,1407,1873,1579,1491,1393,1247,
     +     789,763,49,5,1607,1891,735,1557,1909,1765,1777,1127,813,695,
     +     97,731,1503,1751,333,769,865,693,377,1919,957,1359,1627,1039,
     +     1783,1065,1665,1917,1947,991,1997,841,459,221,327,1595,1881,
     +     1269,1007,129,1413,475,1105,791,1983,1359,503,691,659,691,
     +     343,1375,1919,263,1373,603,1383,297,781,145,285,767,1739,
     +     1715,715,317,1333,85,831,1615,81,1667,1467,1457,1453,1825,
     +     109,387,1207,2039,213,1351,1329,1173/
      DATA (VINIT(I,11),I=590,802)/57,1769,951,183,23,451,1155,1551,
     +     2037,811,635,1671,1451,863,1499,1673,363,1029,1077,1525,277,
     +     1023,655,665,1869,1255,965,277,1601,329,1603,1901,395,65,
     +     1307,2029,21,1321,543,1569,1185,1905,1701,413,2041,1697,725,
     +     1417,1847,411,211,915,1891,17,1877,1699,687,1089,1973,1809,
     +     851,1495,1257,63,1323,1307,609,881,1543,177,617,1505,1747,
     +     1537,925,183,77,1723,1877,1703,397,459,521,257,1177,389,1947,
     +     1553,1583,1831,261,485,289,1281,1543,1591,1123,573,821,1065,
     +     1933,1373,2005,905,207,173,1573,1597,573,1883,1795,1499,1743,
     +     553,335,333,1645,791,871,1157,969,557,141,223,1129,1685,423,
     +     1069,391,99,95,1847,531,1859,1833,1833,341,237,1997,1799,409,
     +     431,1917,363,335,1039,1085,1657,1975,1527,1111,659,389,899,
     +     595,1439,1861,1979,1569,1087,1009,165,1895,1481,1583,29,1193,
     +     1673,1075,301,1081,1377,1747,1497,1103,1789,887,739,1577,313,
     +     1367,1299,1801,1131,1837,73,1865,1065,843,635,55,1655,913,
     +     1037,223,1871,1161,461,479,511,1721,1107,389,151,35,375,1099,
     +     937,1185,1701,769,639,1633/
      DATA (VINIT(I,11),I=803,1018)/1609,379,1613,2031,685,289,975,671,
     +     1599,1447,871,647,99,139,1427,959,89,117,841,891,1959,223,
     +     1697,1145,499,1435,1809,1413,1445,1675,171,1073,1349,1545,
     +     2039,1027,1563,859,215,1673,1919,1633,779,411,1845,1477,1489,
     +     447,1545,351,1989,495,183,1639,1385,1805,1097,1249,1431,1571,
     +     591,697,1509,709,31,1563,165,513,1425,1299,1081,145,1841,
     +     1211,941,609,845,1169,1865,1593,347,293,1277,157,211,93,1679,
     +     1799,527,41,473,563,187,1525,575,1579,857,703,1211,647,709,
     +     981,285,697,163,981,153,1515,47,1553,599,225,1147,381,135,
     +     821,1965,609,1033,983,503,1117,327,453,2005,1257,343,1649,
     +     1199,599,1877,569,695,1587,1475,187,973,233,511,51,1083,665,
     +     1321,531,1875,1939,859,1507,1979,1203,1965,737,921,1565,1943,
     +     819,223,365,167,1705,413,1577,745,1573,655,1633,1003,91,1123,
     +     477,1741,1663,35,715,37,1513,815,941,1379,263,1831,1735,1111,
     +     1449,353,1941,1655,1349,877,285,1723,125,1753,985,723,175,
     +     439,791,1051,1261,717,1555,1757,1777,577,1583,1957,873,331,
     +     1163,313,1,1963,963,1905,821/
      DATA (VINIT(I,11),I=1019,1111)/1677,185,709,545,1723,215,1885,
     +     1249,583,1803,839,885,485,413,1767,425,129,1035,329,1263,
     +     1881,1779,1565,359,367,453,707,1419,831,1889,887,1871,1869,
     +     747,223,1547,1799,433,1441,553,2021,1303,1505,1735,1619,1065,
     +     1161,2047,347,867,881,1447,329,781,1065,219,589,645,1257,
     +     1833,749,1841,1733,1179,1191,1025,1639,1955,1423,1685,1711,
     +     493,549,783,1653,397,895,233,759,1505,677,1449,1573,1297,
     +     1821,1691,791,289,1187,867,1535,575,183/
      DATA (VINIT(I,12),I=338,545)/3915,97,3047,937,2897,953,127,1201,
     +     3819,193,2053,3061,3759,1553,2007,2493,603,3343,3751,1059,
     +     783,1789,1589,283,1093,3919,2747,277,2605,2169,2905,721,4069,
     +     233,261,1137,3993,3619,2881,1275,3865,1299,3757,1193,733,993,
     +     1153,2945,3163,3179,437,271,3493,3971,1005,2615,2253,1131,
     +     585,2775,2171,2383,2937,2447,1745,663,1515,3767,2709,1767,
     +     3185,3017,2815,1829,87,3341,793,2627,2169,1875,3745,367,3783,
     +     783,827,3253,2639,2955,3539,1579,2109,379,2939,3019,1999,
     +     2253,2911,3733,481,1767,1055,4019,4085,105,1829,2097,2379,
     +     1567,2713,737,3423,3941,2659,3961,1755,3613,1937,1559,2287,
     +     2743,67,2859,325,2601,1149,3259,2403,3947,2011,175,3389,3915,
     +     1315,2447,141,359,3609,3933,729,2051,1755,2149,2107,1741,
     +     1051,3681,471,1055,845,257,1559,1061,2803,2219,1315,1369,
     +     3211,4027,105,11,1077,2857,337,3553,3503,3917,2665,3823,3403,
     +     3711,2085,1103,1641,701,4095,2883,1435,653,2363,1597,767,869,
     +     1825,1117,1297,501,505,149,873,2673,551,1499,2793,3277,2143,
     +     3663,533,3991,575,1877,1009,3929,473,3009,2595,3249,675,3593/
      DATA (VINIT(I,12),I=546,752)/2453,1567,973,595,1335,1715,589,85,
     +     2265,3069,461,1659,2627,1307,1731,1501,1699,3545,3803,2157,
     +     453,2813,2047,2999,3841,2361,1079,573,69,1363,1597,3427,2899,
     +     2771,1327,1117,1523,3521,2393,2537,1979,3179,683,2453,453,
     +     1227,779,671,3483,2135,3139,3381,3945,57,1541,3405,3381,2371,
     +     2879,1985,987,3017,3031,3839,1401,3749,2977,681,1175,1519,
     +     3355,907,117,771,3741,3337,1743,1227,3335,2755,1909,3603,
     +     2397,653,87,2025,2617,3257,287,3051,3809,897,2215,63,2043,
     +     1757,3671,297,3131,1305,293,3865,3173,3397,2269,3673,717,
     +     3041,3341,3595,3819,2871,3973,1129,513,871,1485,3977,2473,
     +     1171,1143,3063,3547,2183,3993,133,2529,2699,233,2355,231,
     +     3241,611,1309,3829,1839,1495,301,1169,1613,2673,243,3601,
     +     3669,2813,2671,2679,3463,2477,1795,617,2317,1855,1057,1703,
     +     1761,2515,801,1205,1311,473,3963,697,1221,251,381,3887,1761,
     +     3093,3721,2079,4085,379,3601,3845,433,1781,29,1897,1599,2163,
     +     75,3475,3957,1641,3911,2959,2833,1279,1099,403,799,2183,2699,
     +     1711,2037,727,289,1785,1575,3633,2367,1261,3953,1735,171,
     +     1959/
      DATA (VINIT(I,12),I=753,960)/2867,859,2951,3211,15,1279,1323,599,
     +     1651,3951,1011,315,3513,3351,1725,3793,2399,287,4017,3571,
     +     1007,541,3115,429,1585,1285,755,1211,3047,915,3611,2697,2129,
     +     3669,81,3939,2437,915,779,3567,3701,2479,3807,1893,3927,2619,
     +     2543,3633,2007,3857,3837,487,1769,3759,3105,2727,3155,2479,
     +     1341,1657,2767,2541,577,2105,799,17,2871,3637,953,65,69,2897,
     +     3841,3559,4067,2335,3409,1087,425,2813,1705,1701,1237,821,
     +     1375,3673,2693,3925,1541,1871,2285,847,4035,1101,2029,855,
     +     2733,2503,121,2855,1069,3463,3505,1539,607,1349,575,2301,
     +     2321,1101,333,291,2171,4085,2173,2541,1195,925,4039,1379,699,
     +     1979,275,953,1755,1643,325,101,2263,3329,3673,3413,1977,2727,
     +     2313,1419,887,609,2475,591,2613,2081,3805,3435,2409,111,3557,
     +     3607,903,231,3059,473,2959,2925,3861,2043,3887,351,2865,369,
     +     1377,2639,1261,3625,3279,2201,2949,3049,449,1297,897,1891,
     +     411,2773,749,2753,1825,853,2775,3547,3923,3923,987,3723,2189,
     +     3877,3577,297,2763,1845,3083,2951,483,2169,3985,245,3655,
     +     3441,1023,235,835,3693,3585,327,1003,543,3059,2637/
      DATA (VINIT(I,12),I=961,1111)/2923,87,3617,1031,1043,903,2913,
     +     2177,2641,3279,389,2009,525,4085,3299,987,2409,813,2683,373,
     +     2695,3775,2375,1119,2791,223,325,587,1379,2877,2867,3793,655,
     +     831,3425,1663,1681,2657,1865,3943,2977,1979,2271,3247,1267,
     +     1747,811,159,429,2001,1195,3065,553,1499,3529,1081,2877,3077,
     +     845,1793,2409,3995,2559,4081,1195,2955,1117,1409,785,287,
     +     1521,1607,85,3055,3123,2533,2329,3477,799,3683,3715,337,3139,
     +     3311,431,3511,2299,365,2941,3067,1331,1081,1097,2853,2299,
     +     495,1745,749,3819,619,1059,3559,183,3743,723,949,3501,733,
     +     2599,3983,3961,911,1899,985,2493,1795,653,157,433,2361,3093,
     +     3119,3679,2367,1701,1445,1321,2397,1241,3305,3985,2349,4067,
     +     3805,3073,2837,1567,3783,451,2441,1181,487,543,1201,3735,
     +     2517,733,1535,2175,3613,3019/
      DATA (VINIT(I,13),I=482,680)/2319,653,1379,1675,1951,7075,2087,
     +     7147,1427,893,171,2019,7235,5697,3615,1961,7517,6849,2893,
     +     1883,2863,2173,4543,73,381,3893,6045,1643,7669,1027,1549,
     +     3983,1985,6589,7497,2745,2375,7047,1117,1171,1975,5199,3915,
     +     3695,8113,4303,3773,7705,6855,1675,2245,2817,1719,569,1021,
     +     2077,5945,1833,2631,4851,6371,833,7987,331,1899,8093,6719,
     +     6903,5903,5657,5007,2689,6637,2675,1645,1819,689,6709,7717,
     +     6295,7013,7695,3705,7069,2621,3631,6571,6259,7261,3397,7645,
     +     1115,4753,2047,7579,2271,5403,4911,7629,4225,1209,6955,6951,
     +     1829,5579,5231,1783,4285,7425,599,5785,3275,5643,2263,657,
     +     6769,6261,1251,3249,4447,4111,3991,1215,131,4397,3487,7585,
     +     5565,7199,3573,7105,7409,1671,949,3889,5971,3333,225,3647,
     +     5403,3409,7459,6879,5789,6567,5581,4919,1927,4407,8085,4691,
     +     611,3005,591,753,589,171,5729,5891,1033,3049,6567,5257,8003,
     +     1757,4489,4923,6379,5171,1757,689,3081,1389,4113,455,2761,
     +     847,7575,5829,633,6629,1103,7635,803,6175,6587,2711,3879,67,
     +     1179,4761,7281,1557,3379,2459,4273,4127,7147,35/
      DATA (VINIT(I,13),I=681,877)/3549,395,3735,5787,4179,5889,5057,
     +     7473,4713,2133,2897,1841,2125,1029,1695,6523,1143,5105,7133,
     +     3351,2775,3971,4503,7589,5155,4305,1641,4717,2427,5617,1267,
     +     399,5831,4305,4241,3395,3045,4899,1713,171,411,7099,5473,
     +     5209,1195,1077,1309,2953,7343,4887,3229,6759,6721,6775,675,
     +     4039,2493,7511,3269,4199,6625,7943,2013,4145,667,513,2303,
     +     4591,7941,2741,987,8061,3161,5951,1431,831,5559,7405,1357,
     +     4319,4235,5421,2559,4415,2439,823,1725,6219,4903,6699,5451,
     +     349,7703,2927,7809,6179,1417,5987,3017,4983,3479,4525,4643,
     +     4911,227,5475,2287,5581,6817,1937,1421,4415,7977,1789,3907,
     +     6815,6789,6003,5609,4507,337,7427,7943,3075,6427,1019,7121,
     +     4763,81,3587,2929,1795,8067,2415,1265,4025,5599,4771,3025,
     +     2313,6129,7611,6881,5253,4413,7869,105,3173,1629,2537,1023,
     +     4409,7209,4413,7107,7469,33,1955,2881,5167,6451,4211,179,
     +     5573,7879,3387,7759,5455,7157,1891,5683,5689,6535,3109,6555,
     +     6873,1249,4251,6437,49,2745,1201,7327,4179,6783,623,2779,
     +     5963,2585,6927,5333,4033,285,7467,4443,4917,3/
      DATA (VINIT(I,13),I=878,1070)/4319,5517,3449,813,5499,2515,5771,
     +     3357,2073,4395,4925,2643,7215,5817,1199,1597,1619,7535,4833,
     +     609,4797,8171,6847,793,6757,8165,3371,2431,5235,4739,7703,
     +     7223,6525,5891,5605,4433,3533,5267,5125,5037,225,6717,1121,
     +     5741,2013,4327,4839,569,5227,7677,4315,2391,5551,859,3627,
     +     6377,3903,4311,6527,7573,4905,7731,1909,1555,3279,1949,1887,
     +     6675,5509,2033,5473,3539,5033,5935,6095,4761,1771,1271,1717,
     +     4415,5083,6277,3147,7695,2461,4783,4539,5833,5583,651,1419,
     +     2605,5511,3913,5795,2333,2329,4431,3725,6069,2699,7055,6879,
     +     1017,3121,2547,4603,2385,6915,6103,5669,7833,2001,4287,6619,
     +     955,2761,5711,6291,3415,3909,2841,5627,4939,7671,6059,6275,
     +     6517,1931,4583,7301,1267,7509,1435,2169,6939,3515,2985,2787,
     +     2123,1969,3307,353,4359,7059,5273,5873,6657,6765,6229,3179,
     +     1583,6237,2155,371,273,7491,3309,6805,3015,6831,7819,713,
     +     4747,3935,4109,1311,709,3089,7059,4247,2989,1509,4919,1841,
     +     3045,3821,6929,4655,1333,6429,6649,2131,5265,1051,261,8057,
     +     3379,2179,1993,5655,3063,6381/
      DATA (VINIT(I,13),I=1071,1111)/3587,7417,1579,1541,2107,5085,2873,
     +     6141,955,3537,2157,841,1999,1465,5171,5651,1535,7235,4349,
     +     1263,1453,1005,6893,2919,1947,1635,3963,397,969,4569,655,
     +     6737,2995,7235,7713,973,4821,2377,1673,1,6541/
      
      DATA TAU/0,0,1,3,5,8,11,15,19,23,27,31,35/

C     CHECK PARAMETERS:
      MAX = 30
      ATMOST = 2**30-1
      S = DIMEN
      IF (S.LE.MAXDEG) THEN
         TAUS = TAU(S)
      ELSE
C        RETURN A DUMMY VALUE TO THE CALLING PROGRAM
         TAUS = -1
      END IF

C     FIND NUMBER OF BITS IN ATMOST:
      I = ATMOST
      MAXCOL = 0
   10 MAXCOL = MAXCOL + 1
      I = I/2
      IF (I.GT.0) GOTO 10
C     INITIALIZE ROW 1 OF V
      DO I = 1, MAXCOL
         V(1,I) = 1
      ENDDO

C     INITIALIZE REMAINING ROWS OF V:
      DO I = 2, S
C        THE BIT PATTERN OF POLYNOMIAL I GIVES ITS FORM
C        FIND DEGREE OF POLYNOMIAL I FROM BINARY ENCODING
         J = POLY(I)
         M = 0
   30    J = J/2
         IF (J.GT.0) THEN
            M = M + 1
            GOTO 30
         ENDIF
C        WE EXPAND THIS BIT PATTERN TO SEPARATE COMPONENTS
C        OF THE LOGICAL ARRAY INCLUD.
         J = POLY(I)
         DO K = M, 1, -1
            INCLUD(K) = (MOD(J, 2).EQ.1)
            J = J/2
         ENDDO
C        THE LEADING ELEMENTS OF ROW I COME FROM VINIT
         DO J = 1, M
            V(I, J) = VINIT(I, J)
         ENDDO
C        CALCULATE REMAINING ELEMENTS OF ROW I AS EXPLAINED
C        IN BRATLEY AND FOX, SECTION 2
         DO J = M + 1,MAXCOL
            NEWV = V(I, J-M)
            L = 1
            DO K = 1, M
               L = 2*L
               IF (INCLUD(K)) NEWV = IEOR(NEWV, L*V(I, J-K))
C              IF A FULL-WORD EXCLUSIVE-OR, SAY .IEOR., IS AVAILABLE,
C              THEN REPLACE THE PRECEDING STATEMENT BY
            ENDDO
            V(I, J) = NEWV
         ENDDO
      ENDDO

C     MULTIPLY COLUMNS OF V BY APPROPRIATE POWER OF 2:
      L = 1
      DO J = MAXCOL-1, 1, -1
         L = 2*L
         DO I = 1, S
            V(I, J) = V(I, J)*L
         ENDDO
      ENDDO

C>>> SCRAMBLING START
      IF (IFLAG .EQ. 0) THEN
         DO I = 1, S
            DO J = 1,MAXCOL 
               SV(I, J) = V(I, J)
            ENDDO
            SHIFT(I) = 0
         ENDDO
         LL= 2**MAXCOL
      ELSE             
         IF ((IFLAG .EQ. 1) .OR. (IFLAG .EQ. 3)) THEN
         CALL SGENSCRML(MAX, LSM, SHIFT, S, MAXCOL, iSEED)
         DO I = 1,S
            DO J = 1,MAXCOL
               L = 1
               TEMP2 = 0
               DO P = MAX,1,-1
                  TEMP1 = 0
                  DO K = 1,MAXCOL
                     TEMP01 = IBITS(LSM(I,P),K-1,1)*IBITS(V(I,J),K-1,1)
                     TEMP1 = TEMP1 + TEMP01
                  ENDDO
                  TEMP1 = MOD(TEMP1, 2)
                  TEMP2 = TEMP2+TEMP1*L   
                  L = 2 * L
               ENDDO
               SV(I, J) = TEMP2
            ENDDO
         ENDDO
         LL= 2**MAX
      ENDIF
         IF ((IFLAG .EQ. 2) .OR. (IFLAG .EQ. 3)) THEN
            CALL SGENSCRMU(USM, USHIFT, S, MAXCOL, iSEED) 
            IF (IFLAG .EQ. 2) THEN
               MAXX = MAXCOL
            ELSE
               MAXX = MAX
            ENDIF    
            DO I = 1, S
               DO J = 1, MAXCOL
                  P = MAXX
                  DO K = 1, MAXX
                     IF (IFLAG .EQ. 2) THEN
                        TV(I,P,J) = IBITS(V(I,J),K-1,1)
                     ELSE
                        TV(I,P,J) = IBITS(SV(I,J),K-1,1) 
                     ENDIF 
                     P = P-1
                  ENDDO
               ENDDO     
               DO PP = 1, MAXCOL 
                  TEMP2 = 0 
                  TEMP4 = 0
                  L = 1
                  DO J = MAXX, 1, -1
                     TEMP1 = 0
                     TEMP3 = 0
                     DO P = 1, MAXCOL
                        TEMP1 = TEMP1 + TV(I,J,P)*USM(P,PP)
                        IF (PP .EQ. 1) THEN
                           TEMP3 = TEMP3 + TV(I,J,P)*USHIFT(P)
                        ENDIF 
                     ENDDO
                     TEMP1 = MOD(TEMP1,2)
                     TEMP2 = TEMP2 + TEMP1*L
                     IF (PP .EQ. 1) THEN 
                        TEMP3 = MOD(TEMP3,2)
                        TEMP4 = TEMP4 + TEMP3*L
                     ENDIF  
                     L = 2*L
                  ENDDO
                  SV(I, PP) = TEMP2
                  IF (PP .EQ. 1) THEN
                     IF (IFLAG .EQ. 3) THEN
                        SHIFT(I) = IEOR(TEMP4, SHIFT(I))           
                     ELSE
                        SHIFT(I) = TEMP4
                     ENDIF  
                  ENDIF
               ENDDO 
            ENDDO
            LL = 2**MAXX
         ENDIF
      ENDIF 
C <<< END OF SCRAMBLING

C     RECIPD IS 1/(COMMON DENOMINATOR OF THE ELEMENTS IN SV)
      RECIPD = 1.0 / LL

C     SET UP FIRST VECTOR AND VALUES FOR "GOSOBL"
      COUNT = 0
      DO I = 1, S
         QUASI(I) = SHIFT(I)*RECIPD
      ENDDO
      RETURN
      END


C ------------------------------------------------------------------------------


      SUBROUTINE SGENSCRML(MAX, LSM, SHIFT, S, MAXCOL, iSEED)

C     GENERATING LOWER TRIANGULAR SCRAMBLING MATRICES AND SHIFT VECTORS.
      REAL*4 UNIS
      INTEGER S,MAXCOL,P,I,J,MAX,TEMP,STEMP,L,LL
      INTEGER SHIFT(1111),LSM(1111,31)
      INTEGER iSEED
      
      DO P = 1, S
         SHIFT(P) = 0
         L = 1
         DO I = MAX, 1, -1
            LSM(P, I) = 0
            STEMP =  MOD((INT(UNIS(iSEED)*1000.0)), 2)
            SHIFT(P) = SHIFT(P) + STEMP*L
            L = 2 * L
            LL = 1
            DO J = MAXCOL, 1, -1
               IF (J .EQ. I) THEN
                  TEMP = 1
               ELSEIF (J .LT. I)  THEN 
                  TEMP = MOD((INT(UNIS(iSEED)*1000.0)), 2)
               ELSE
                  TEMP = 0
               ENDIF
               LSM(P ,I) = LSM(P, I) + TEMP*LL
               LL = 2 * LL            
            ENDDO
         ENDDO 
      ENDDO
      RETURN
      END   

     
C ------------------------------------------------------------------------------


      SUBROUTINE SGENSCRMU(USM, USHIFT, S, MAXCOL, iSEED)

C     GENERATING UPPER TRIANGULAR SCRMABLING MATRICES AND SHIFT VECTORS.
      REAL*4 UNIS
      INTEGER USM(31,31),MAXCOL,I,J
      INTEGER USHIFT(31),S,TEMP,STEMP
      INTEGER iSEED
      
      DO I = 1, MAXCOL
         STEMP =  MOD((INT(UNIS(iSEED)*1000.0)), 2)
         USHIFT(I) = STEMP               
         DO J = 1, MAXCOL
            IF (J .EQ. I) THEN
               TEMP = 1
            ELSEIF (J .GT. I)  THEN 
               TEMP = MOD((INT(UNIS(iSEED)*1000.0)), 2)
            ELSE
               TEMP = 0
            ENDIF
            USM(I, J) = TEMP        
         ENDDO
      ENDDO 
      RETURN
      END   


C-------------------------------------------------------------------------------
      
      
      REAL*4 FUNCTION UNIS(IX)
C       PORTABLE PSEUDORANDOM NUMBER
C       GENERATOR IMPLEMENTING THE RECURSION
C       IX=16807*IX MOD(2**31-1)
C       UNIF=IX/(2**31-1)
C       USING ONLY 32 BITS INCLUDING SIGN
C       INPUT:
C        IX =INTEGER STRICTLY BETWEEN 0 AND 2** 31 -1
C       OUTPUTS:
C        IX=NEW PSEUDORANDOM INTEGER
C           STRICTLY BETWEEN 0 AND 2**31-1
C        UNIF=UNIFORM VARIATE (FRACTION)
C           STRICTLY BETWEEN 0 AND 1
C      FOR JUSTIFICATION, SEE P. BRATLEY,
C      B.L. FOX, AND L.E. SCHRAGE (1983)
C      "A GUIDE TO SIMULATION"
C      SPRINGER-VERLAG, PAGES 201-202
      INTEGER K1,IX
      K1 = IX/127773
      IX = 16807*(IX-K1*127773)-K1*2836
      IF (IX.LT.0) IX=IX+2147483647
      UNIS = IX*4.656612875E-10
      RETURN
      END


C-------------------------------------------------------------------------------   


      SUBROUTINE NEXTSOBOL(DIMEN, QUASI, LL, COUNT, SV)

C     GENERATES A NEW QUASIRANDOM VECTOR WITH EACH CALL. IT ADAPTS THE 
C     IDEAS OF ANTONOV AND SALEEV, USSR COMPUT. MATHS. MATH. PHYS. 19, 
C     (1980), 252-256. "INITSOBOL" MUST BE CALLED BEFORE CALLING "NEXTSOBOL". 
C     ARGUMENTS:
C       DIMEN     - DIMENSION OF THE SEQUENCY
C       QUASI     - LAST POINT IN THE SEQUENDE
C       LL        - COMMON DENOMINATOR OF THE ELEMENTS IN SV
C       COUNT     - SEQUENCE NUMBER OF THE CALL
      
      INTEGER DIMEN,MAXBIT,I,L,COUNT
      PARAMETER (MAXBIT=30)
      INTEGER SV(DIMEN,MAXBIT)
      REAL*8 QUASI(DIMEN)
      INTRINSIC MOD, IEOR
      
      L = 0
      I = COUNT
   10 L = L + 1
      IF (MOD(I, 2).EQ.1) THEN
         I = I/2
         GOTO 10
      END IF

C     CALCULATE THE NEW COMPONENTS OF QUASI,
C     FIRST THE NUMERATORS, THEN NORMALIZED
      DO I = 1, DIMEN
         QUASI(I) = REAL(IEOR(INT(QUASI(I)*LL), SV(I, L)))/LL
      ENDDO

      COUNT = COUNT + 1
      RETURN
      END

      
C ------------------------------------------------------------------------------
   

      SUBROUTINE TESTSOBOL()

C     TESTROUTINE, CALLED FROM THE FORTRAN MAIN PROGRAM
      INTEGER MAXBIT,DIMEN,TRANSFORM
      PARAMETER (N1=20,N2=N1/2,DIMEN=5,MAXBIT=30)
      INTEGER LL,COUNT,SV(DIMEN,MAXBIT)
      REAL*8 QN1(N1,DIMEN),QN2(N2,DIMEN),QUASI(DIMEN)
      INTEGER iSEED, iSEED1

      TRANSFORM = 1
      IFLAG = 3
      iSEED1 = 4711
           
      INIT = 1
      iSEED = iSEED1
      CALL SOBOL(QN1, N1, DIMEN, QUASI ,LL, COUNT, SV,
     &     IFLAG, iSEED, INIT, TRANSFORM)

      WRITE (*,*) 
      WRITE (*,7) "N/DIMEN:", (J, J=1,DIMEN,INT(DIMEN/5))   
      DO I=1, N1, INT(N1/(2*10))
         WRITE (*,8) I, (QN1(I,J), J=1, DIMEN, INT(DIMEN/5))
      ENDDO

      INIT=1
      iSEED = iSEED1
      CALL SOBOL(QN2, N2, DIMEN, QUASI, LL, COUNT, SV,
     &     IFLAG, iSEED, INIT, TRANSFORM)
      WRITE (*,*) 
      WRITE (*,7) "N/DIMEN:", (J, J=1,DIMEN,INT(DIMEN/5))   
      DO I=1, N2, INT(N2/10)
         WRITE (*,8) I, (QN2(I,J), J=1, DIMEN, INT(DIMEN/5))
      ENDDO

      INIT = 0
      CALL SOBOL(QN2, N2, DIMEN, QUASI, LL, COUNT, SV,
     &     IFLAG, iSEED, INIT, TRANSFORM)
      WRITE (*,*) 
      WRITE (*,7) "N/DIMEN:", (J, J=1,DIMEN,INT(DIMEN/5))   
      DO I=1, N2, INT(N2/10)
         WRITE (*,8) I+N2, (QN2(I,J), J=1, DIMEN, INT(DIMEN/5))
      ENDDO

 7    FORMAT(1H ,A8, 10I10)
 8    FORMAT(1H ,I8, 10F10.6)

      RETURN
      END


C ------------------------------------------------------------------------------


C     program mainsobol
C     call testsobol()
C     end


C ------------------------------------------------------------------------------


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