#include <iostream>
#include <vector>
#include <string>
#include <numeric>
#include <algorithm>
using namespace std;
typedef pair<int, int> pii;
int N;
bool dp[10001][10001];
string ans = "impossible";
int main(void) {
	for (int i = 0; i < 10000; ++i) for (int j = 0; j < 10000; ++j) int i = 0;
	return 0;
}