#include <string>

#include <cstdio>

inline constexper int TABLE[][10] = {
	{0, 3, 1, 7, 5, 9, 8, 6, 4, 2},
	{7, 0, 9, 2, 1, 5, 4, 8, 6, 3},
	{4, 2, 0, 6, 8, 7, 1, 3, 5, 9},
	{1, 7, 5, 0, 9, 8, 3, 4, 2, 6},
	{6, 1, 2, 3, 0, 4, 5, 9, 7, 8},
	{3, 6, 7, 4, 2, 0, 9, 5, 8, 1},
	{5, 8, 6, 9, 7, 2, 0, 1, 3, 4},
	{8, 9, 4, 5, 3, 6, 2, 0, 1, 7},
	{9, 4, 3, 8, 6, 1, 7, 2, 0, 5},
	{2, 5, 8, 1, 4, 3, 6, 7, 9, 0},
};

[[nodiscard]] bool damm(std::string s) noexcept {
	int interim = 0;
	for (const auto c : s) {
		interim = TABLE[interim][c - '0'];
	}
	return interim == 0;
}

int main() {
	for (const auto num : { 5724, 5727, 112946, 112949 }) {
		if (damm(std::to_string(num))) {
	 	 	std::printf("%6d is valid\n", num);
		}	
		else std::printf("%6d is invalid\n", num);
	}
}