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LowDiscrepancy.f
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LowDiscrepancy.f
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C PART I: HALTON SEQUENCE
C PART II: SOBOL SEQUENCE
C###############################################################################
C PART I: HALTON SEQUENCE:
C-------------------------------------------------------------------------------
C @file LowDiscrepancy.f
C @brief Halton sequence
C
C @author Diethelm Wuertz
C @author Christophe Dutang
C @author Yohan Chalabi
C
C Copyright (C) Sept. 2002, Diethelm Wuertz, ETH Zurich. All rights
C reserved. slightly modified (better accuracy and speed) by
C Christophe Dutang in October 2009. Delcared all variables and
C functions to avoid troubles with new version of gfortran by Yohan
C Chalabi in June 2011.
C
C The new BSD License is applied to this software.
C Copyright (c) Diethelm Wuertz, ETH Zurich. All rights reserved.
C
C Redistribution and use in source and binary forms, with or without
C modification, are permitted provided that the following conditions are
C met:
C
C - Redistributions of source code must retain the above copyright
C notice, this list of conditions and the following disclaimer.
C - Redistributions in binary form must reproduce the above
C Copyright notice, this list of conditions and the following
C disclaimer in the documentation and/or other materials provided
C with the distribution.
C - Neither the name of the ETH Zurich nor the names of its contributors
C may be used to endorse or promote products derived from this software
C without specific prior written permission.
C
C THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
C "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
C LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
C A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
C OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
C SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
C LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
C DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
C THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
C (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
C OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
C
C-------------------------------------------------------------------------------
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
IMPLICIT NONE
INTEGER DIMEN, BASE(DIMEN), ITER(DIMEN), OFFSET, DIGIT
DOUBLE PRECISION QUASI(DIMEN), HALF
INTRINSIC MOD
INTEGER NC, I, K, M, N, NB
C INIT BASE FROM PRIMES - THIS IMPLEMENTS A SIMPLE 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.
IMPLICIT NONE
INTEGER DIMEN, BASE(DIMEN), ITER(DIMEN), OFFSET, DIGIT
DOUBLE PRECISION QUASI(DIMEN), HALF
INTRINSIC MOD
INTEGER NB
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 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 SEQUENCE
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
IMPLICIT NONE
INTEGER N, DIMEN, OFFSET, INIT, TRANSFORM
INTEGER BASE(DIMEN)
DOUBLE PRECISION QN(N,DIMEN), QUASI(DIMEN)
DOUBLE PRECISION HQNORM
INTEGER I, J
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:
IF (TRANSFORM.EQ.0) THEN
DO I=1, N
CALL NEXTHALTON(DIMEN, QUASI, BASE, OFFSET)
DO J = 1, DIMEN
QN(I, J) = QUASI(J)
ENDDO
ENDDO
ELSE
DO I=1, N
CALL NEXTHALTON(DIMEN, QUASI, BASE, OFFSET)
DO J = 1, DIMEN
QN(I, J) = HQNORM(QUASI(J))
ENDDO
ENDDO
ENDIF
RETURN
END
C-------------------------------------------------------------------------------
DOUBLE PRECISION FUNCTION HQNORM(P)
IMPLICIT NONE
C USED TO CALCULATE HALTON NORMAL DEVIATES:
DOUBLE PRECISION P,R,T,A,B, EPS
DOUBLE PRECISION P0,P1,P2,P3,P4, Q0,Q1,Q2,Q3,Q4
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()
IMPLICIT NONE
INTEGER N1,N2,DIMEN,OFFSET,TRANSFORM
PARAMETER (N1=20,N2=N1/2,DIMEN=5)
INTEGER BASE(DIMEN)
DOUBLE PRECISION QN1(N1,DIMEN),QN2(N2,DIMEN)
INTEGER J, I, INIT
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:
C--------------------------------------------------------------------------
C @file LowDiscrepancy.f
C @brief Sobol sequence
C
C @author Diethelm Wuertz
C
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 @author Christophe Dutang
C
C Copyright (C) Sept. 2002, Diethelm Wuertz, ETH Zurich. All rights reserved.
C slightly modified (better accuracy and speed) by Christophe Dutang in October 2009.
C
C The new BSD License is applied to this software.
C Copyright (c) Diethelm Wuertz, ETH Zurich. All rights reserved.
C
C Redistribution and use in source and binary forms, with or without
C modification, are permitted provided that the following Conditions are
C met:
C
C - Redistributions of source Code must retain the above Copyright
C notice, this list of Conditions and the following disclaimer.
C - Redistributions in binary form must reproduce the above
C Copyright notice, this list of Conditions and the following
C disclaimer in the documentation and/or other materials provided
C with the distribution.
C - Neither the name of the ETH Zurich nor the names of its Contributors
C may be used to endorse or promote products derived from this software
C without specific prior written permission.
C
C THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
C "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
C LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
C A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
C OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
C SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
C LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
C DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
C THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
C (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
C OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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 SEQUENCE
C QUASI - LAST POINT IN THE SEQUENCE
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 - INITIALIZATION FLAG, 0 NEXT, 1 RE-INITIALIZE
C TRANSFORM - FLAG, 0 FOR UNIFORM, 1 FOR NORMAL DISTRIBUTION
IMPLICIT NONE
INTEGER MAXBIT,N,DIMEN,INIT,TRANSFORM
PARAMETER (MAXBIT=30)
INTEGER LL,COUNT,SV(DIMEN,MAXBIT)
INTEGER iSEED, IFLAG, I, J
DOUBLE PRECISION QN(N,DIMEN), QUASI(DIMEN)
DOUBLE PRECISION SQNORM
EXTERNAL SQNORM
IF (INIT.EQ.1) THEN
CALL INITSOBOL(DIMEN, QUASI, LL, COUNT, SV, IFLAG, iSEED)
ENDIF
C GENERATE THE NEXT "N" QUASI RANDOM NUMBERS:
IF (TRANSFORM.EQ.0) THEN
DO I=1, N
CALL NEXTSOBOL(DIMEN, QUASI, LL, COUNT, SV)
DO J = 1, DIMEN
QN(I, J) = QUASI(J)
ENDDO
ENDDO
ELSE
DO I=1, N
CALL NEXTSOBOL(DIMEN, QUASI, LL, COUNT, SV)
DO J = 1, DIMEN
QN(I, J) = SQNORM(QUASI(J))
ENDDO
ENDDO
ENDIF
RETURN
END
C-------------------------------------------------------------------------------
DOUBLE PRECISION FUNCTION SQNORM(P)
IMPLICIT NONE
C USED TO CALCULATE SOBOL NORMAL DEVIATES
DOUBLE PRECISION P,R,T,A,B, EPS
DOUBLE PRECISION P0,P1,P2,P3,P4, Q0,Q1,Q2,Q3,Q4
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 = 1.0D0 - 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, THESE 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 SEQUENCE
C QUASI - LAST POINT IN THE SEQUENCE
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
IMPLICIT NONE
INTEGER MAXDIM,MAXDEG,MAXBIT,IFLAG
C C 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)
C C INTEGER TEMP1,TEMP2,TEMP4
INTEGER TEMP1,TEMP2,TEMP3,TEMP4
INTEGER SHIFT(1111),LSM(1111,31),TV(1111,31,31)
DOUBLE PRECISION QUASI(DIMEN),RECIPD
INTEGER iSEED
LOGICAL INCLUD(MAXDEG)
INTRINSIC MOD, IEOR
INTEGER LL, MAXX, MAX, TEMP01
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,