#include <bits/stdc++.h>
 
using namespace std;
 
const int MaxN = (int)2e5 + 10;
const int INF = (int)1e9;
const int MOD = (int)1e9 + 7;

int n, a[MaxN], b[MaxN];

void solve() {
	scanf("%d", &n);
	int mx = 0, pos = -1;
	for (int i = 1; i <= n; ++i) {
		scanf("%d", &a[i]);
		mx = max(mx, a[i]);
		if (mx == a[i]) {
			pos = i;
		}
	}
	bool can = true;
	for (int i = 1; i <= n; ++i) {
		if (a[i] == -1 || a[i] >= 1 && a[i] == a[pos] - (pos - i)) {
			continue;
		}
		can = false;
	}
	if (can) {
		cout << "inf\n";
		return;
	}
	set <int> s;
	for (int i = 1; i <= n; ++i) {
		if (a[i] != -1) {
			s.insert (i - a[i] + 1);
		}
	}
	assert (s.size() >= 2);
	int last = -1e9;
	int res = 0;
	for (auto &it : s) {
		if (last != -1e9) {
			res = __gcd(res, it - last);
		}
		last = it;
	}
	for (int i = 1; i <= n; ++i) {
		b[i] = (a[pos] - (pos - i)) % res;
		if (b[i] <= 0) {
			b[i] += res;
		}
		if (a[i] != b[i] && a[i] != -1) {
			cout << "impossible\n";
			return;
		}
	}
	cout << res << "\n";
}
 
int main() {
//	freopen("input.txt", "r", stdin);
	int t;
	scanf("%d\n", &t);
	while (t --> 0) {
		solve();
	}
	return 0;
}