#include <bits/stdc++.h>
// #pragma GCC optimize("Ofast,unroll-loops")
using namespace std;
using i64 = long long;
using i128 = __int128;
using ui64 = unsigned long long;
using ui32 = unsigned int;
#define x first
#define y second
typedef pair<i64, i64> PII;
constexpr int mod = 998244353;
constexpr int N = 1e6 + 10, M = 2e6 + 10;
void slove() {
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    int c = -1;
    for (int i = 0; i < n; i++) {
        // cout << ((a[i] - a[((i - 1) + n) % n]) % n + n) % n << "!\n";
        if (c == -1 || c == ((a[i] - a[((i - 1) + n) % n]) % n + n) % n) {
            c = ((a[i] - a[((i - 1) + n) % n]) % n + n) % n;
        }
        else {
            cout << "-1\n";
            return;
        }
    }
    if (c == 0) {
        cout << 2 * n - 1 << '\n';
    }
    else cout << c * 2 - 1 << '\n';
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t = 1;
    cin >> t;
    while (t--) { 
        slove();
    }
    
    return 0;
}