#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <string.h>

struct permutation {
    int p[12];
};
static bool permutations_equal(struct permutation a, struct permutation b) {
    return memcmp(a.p, b.p, sizeof(a.p)) == 0;
}
static struct permutation compose(struct permutation a, struct permutation b) {
    struct permutation p;
    for (int i = 0; i < 12; ++i)
        p.p[i] = a.p[b.p[i]];
    return p;
}
static uint16_t apply(struct permutation p, uint16_t v) {
    uint16_t r = 0;
    for (int i = 0; i < 12; ++i) {
        if (v & (1 << i))
            r |= 1 << p.p[i];
    }
    return r;
}
static const struct permutation I = { .p = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 } }; // identity
static const struct permutation F = { .p = { 0, 4, 1, 2, 7, 8, 5, 3, 11, 9, 6, 10 } }; // rotation around a face (order 5)
static const struct permutation V = { .p = { 2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10 } }; // rotation around a vertex (order 3)

static const uint16_t visible_faces = 0x9f; // looking out from face 0, faces 0, 1, 2, 3, 4, and 7 are visible

static int compare_uint16(const void *a, const void *b) {
    return (int)(*(const uint16_t *)b) - (int)(*(const uint16_t *)a);
}

static void insert_permutation(struct permutation *a, int *length, struct permutation p) {
    for (int i = 0; i < *length; ++i) {
        if (permutations_equal(p, a[i]))
            return;
    }
    a[(*length)++] = p;
}

int main() {
    struct permutation rotations[60] = { I };
    int cursor = 0;
    int length = 1;
    while (cursor < length) {
        struct permutation p = rotations[cursor++];
        insert_permutation(rotations, &length, compose(F, p));
        insert_permutation(rotations, &length, compose(V, p));
    }
    uint16_t permuted_colors[60];
    for (uint16_t i = 0; i < (1 << 12); ++i) {
        for (int j = 0; j < 60; ++j)
            permuted_colors[j] = apply(rotations[j], i) & visible_faces;
        qsort(permuted_colors, 60, sizeof(uint16_t), compare_uint16);
        bool unique = true;
        for (int j = 1; j < 60 && unique; ++j) {
            if (permuted_colors[j] == permuted_colors[j - 1])
                unique = false;
        }
        if (unique)
            printf("%x\n", i);
    }
}