#include <array>
#include <cstdint>
#include <iostream>
#include <utility>
#include <vector>

using Towers = std::array<std::vector<int>, 3>;

// Plays the one legal move between towers a and b, whichever way round it goes.
void move_between(Towers& towers, int a, int b) {
    if (towers[a].empty() || (!towers[b].empty() && towers[b].back() < towers[a].back())) {
        std::swap(a, b);
    }
    int disk = towers[a].back();
    towers[a].pop_back();
    towers[b].push_back(disk);
    std::cout << "Move disk " << disk << " from " << "ABC"[a] << " to " << "ABC"[b] << '\n';
}

void hanoi_pairs(int n) {
    Towers towers;
    for (int disk = n; disk >= 1; disk--) {
        towers[0].push_back(disk);
    }
    // The same three pairs of towers, over and over. For an odd n, B and C trade places.
    const int b = n % 2 == 0 ? 1 : 2;
    const int c = 3 - b;
    const std::uint64_t total = (std::uint64_t{1} << n) - 1;
    for (std::uint64_t m = 0; m < total; m++) {
        switch (m % 3) {
            case 0: move_between(towers, 0, b); break;
            case 1: move_between(towers, 0, c); break;
            case 2: move_between(towers, b, c); break;
        }
    }
}

int main() {
    hanoi_pairs(3);
}