UVa 12024 - Hats

// UVa 12024 - Hats

#include <iostream>
#include <string.h>
using namespace std;

#define datatype signed long long int

int main() {

	datatype fact[13];
	fact[0] = 1;
	for (int i = 1; i <= 12; i++)
		fact[i] = fact[i - 1] * i;

	datatype C[13][13];
	memset(C, 0, sizeof(C));
	for (int n = 0; n <= 12; n++)
		C[n][0] = 1;
	for (int n = 1; n <= 12; n++)
		for (int k = 1; k <= n; k++)
			C[n][k] = C[n - 1][k] + C[n - 1][k - 1];

	int cases;
	for (cin >> cases; cases; cases--) {
		int n;
		cin >> n;
		datatype a = 0;
		for (int i = 1; i <= n; i++) {
			datatype Li = 0;
			int sign = -1;
			for (int j = 0; j < i; j++) {
				sign *= -1;
				Li += sign * C[i - 1][j] * fact[n - j - 1];
			}
			a += Li;
		}
		datatype b = fact[n];
		cout << b - a << "/" << b << endl;
	}

	return 0;
}