#include <bits/stdc++.h>
using namespace std;
// Provided by the grader
long long collisions(vector<long long> x);
int hack() {
for (long long k = 1; k <= 1000000; k++) {
vector<long long> x = {0, k};
long long c = collisions(x);
if (c == 1) {
return (int)k; // k is the hidden n
}
}
// Fallback (should not happen in small-n tests)
return -1;
}
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