/*
　三角数, 四角数, 五角数, 六角数, 七角数, 八角数が全て表れる6つの巡回する4桁の数からなる
　唯一の順序集合の和を求めよ.
*/

#include <stdio.h>

#define BEGINTRI    45
#define ENDTRI      140
#define BEGINSQU    32
#define ENDSQU      99
#define BEGINPEN    26
#define ENDPEN      81
#define BEGINHEX    23
#define ENDHEX      70
#define BEGINHEP    21
#define ENDHEP      63
#define BEGINOCT    19
#define ENDOCT      58

int list[6][100][100];
int root;

int triangular(int n) {

    return n * (n + 1) / 2;
}

int square(int n) {

    return n * n;
}

int pentagonal(int n) {

    return n * (3 * n - 1) / 2;
}

int hexagonal(int n) {

    return n * (2 * n - 1);
}

int heptagonal(int n) {

    return n * (5 * n - 3) / 2;
}

int octagonal(int n) {

    return n * (3 * n - 2);
}

void makeList(void) {
    int i;
    int twoUpperIdx[100] = { 0 };
    int num;
    int twoUpper;

    for( i = BEGINSQU; i <= ENDSQU; i++ ) {
        num = square(i);
        if( num % 100 < 10 ) continue;
        twoUpper = num / 100;
        list[1][twoUpper][twoUpperIdx[twoUpper]] = num;
        twoUpperIdx[twoUpper]++;
    }

    for( i = 0; i < 100; i++ ) twoUpperIdx[i] = 0;
    for( i = BEGINPEN; i <= ENDPEN; i++ ) {
        num = pentagonal(i);
        if( num % 100 < 10 ) continue;
        twoUpper = num / 100;
        list[2][twoUpper][twoUpperIdx[twoUpper]] = num;
        twoUpperIdx[twoUpper]++;
    }

    for( i = 0; i < 100; i++ ) twoUpperIdx[i] = 0;
    for( i = BEGINHEX; i <= ENDHEX; i++ ) {
        num = hexagonal(i);
        if( num % 100 < 10 ) continue;
        twoUpper = num / 100;
        list[3][twoUpper][twoUpperIdx[twoUpper]] = num;
        twoUpperIdx[twoUpper]++;
    }

    for( i = 0; i < 100; i++ ) twoUpperIdx[i] = 0;
    for( i = BEGINHEP; i <= ENDHEP; i++ ) {
        num = heptagonal(i);
        if( num % 100 < 10 ) continue;
        twoUpper = num / 100;
        list[4][twoUpper][twoUpperIdx[twoUpper]] = num;
        twoUpperIdx[twoUpper]++;
    }

    for( i = 0; i < 100; i++ ) twoUpperIdx[i] = 0;
    for( i = BEGINOCT; i <= ENDOCT; i++ ) {
        num = octagonal(i);
        if( num % 100 < 10 ) continue;
        twoUpper = num / 100;
        list[5][twoUpper][twoUpperIdx[twoUpper]] = num;
        twoUpperIdx[twoUpper]++;
    }

    return;
}

int rec(int num, int check) {
    int i, j;
    int rep;

    if( check == 0x3f ) {
        if( num % 100 == root / 100 ) {
            return num;
        } else {
            return -1;
        }
    }

    for( i = 0; i <= 5; i++ ) {
        if( 1 << i & check ) continue;

        for( j = 0; list[i][num % 100][j] != 0; j++ ) {
            rep = rec(list[i][num % 100][j], check | 1 << i);
            if( rep != -1 ) return rep + num;
        }
    }

    return -1;
}

void problem61(void) {
    int i;
    int num;
    int rep;

    makeList();

    for( i = BEGINTRI; i <= ENDTRI; i++ ) {
        num = triangular(i);
        root = num;
        rep = rec(num, 1);
        if( rep != -1 ) {
            printf("%d\n", rep);
        }
    }

    return;
}

int main(void) {

    problem61();

    return 0;
}

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