为什么n>16就会re？

#include<bits/stdc++.h>
using namespace std;
int a[100005];
int jc(int n) {
	int sum = 1;
	for (int i = 1; i <= n; i++) sum *= i;
	return sum;
}
int main() {
	int n, cnt = 0;
	cin >> n;
	while (1) {
		cnt++;
		int flag = 0;
		a[cnt] = 1;
		if (jc(cnt) <= n) a[jc(cnt)] = 1;
//		cout << setw(3) << cnt << ":";
//		for (int i = 1; i <= n; i++) cout << a[i] << ' ';
//		cout << endl;
		for (int i = 1; i <= n; i++) {
			if (a[i] == 0) {
				flag = 1;
				break;
			}
		}
		if (flag == 0) {
			cout << cnt;
			return 0;
		}
	}
}