Есть ли цикл?

#include <bits/stdc++.h>

using namespace std;

const int N = 105;

int n;
int used[N];
int a[N][N];
bool cycle = false;

void dfs(int v, int start) {
    used[v] = 1;
    for (int i = 1; i <= n; i++) {
        if (a[v][i] == 1 && i == start) {
            cycle = true;
        }
        if (a[v][i] == 1 && used[i] == 0) {
            dfs(i, start);
        }
    }
}

int main(){
    cin >> n;

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            cin >> a[i][j];
        }
    }

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            used[j] = 0;
        }
        dfs(i, i);
    }

    cout << cycle << endl;
}