Sequence Decreasing

Gracie Abrams - That's So True

An array $b$ of non-negative integers is called good if it can be turned into a non-empty array consisting only of zeros by performing the following operation any number of times (possibly zero):

1. choose a non-empty subarray$^{\text{∗}}$ of $b$ in which all elements are positive;
2. decrease each element of this subarray by $1$;
3. choose one element of this subarray and remove it from $b$, without changing the order of the remaining elements.

You are given an array $a$ of $n$ non-negative integers. Find the maximum length of a good subsequence$^{\text{†}}$ of $a$, or report that $a$ has no good subsequence.

$^{\text{∗}}$An array $c$ is a subarray of an array $b$ if $c$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

$^{\text{†}}$A sequence $c$ is a subsequence of a sequence $a$ if $c$ can be obtained from $a$ by the deletion of several (possibly, zero or all) elements from arbitrary positions.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output a single integer — the maximum length of a good subsequence of $a$, or $0$ if no such subsequence exists.

Note

In the first test case, the array $a$ itself is good, since it is non-empty and consists only of zeros. Thus, the answer is $1$.

In the second test case, it can be shown that $a$ has no good subsequence. Thus, the answer is $0$.

4
1
0
1
1
3
5 3 4
5
2 1 1 0 3

1
0
0
5