Beautiful Sequence

#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 9;
const int INF = 1e17 + 9;

int A[N];

void solve () {
    int n;
    cin >> n;

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

    vector <int> dp (n + 1, INF);
    dp[0] = -INF;

    for (int i = 1; i <= n; i++) {
        if (A[i] < 0)
            continue;

        int j = upper_bound (dp.begin(), dp.end(), A[i]) - dp.begin();
        if (dp[j - 1] <= A[i] && A[i] < dp[j])
            dp[j] = A[i];
    }

    int len = 0;
    for (int i = 1; i <= n; i++) {
        if (dp[i] < INF)
            len = i;
    }

    cout << n - len << "\n";
    return;
}

int main () {
    int t;
    cin >> t;

    while (t--)
        solve ();

    return 0;
}