github.com/captn3m0/codechef.git

---
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---
Chef has a sequence $A_1, A_2, \ldots, A_N$. For a positive integer $M$, sequence $B$ is defined as $B = A*M$ that is, appending $A$ exactly $M$ times. For example, If $A = [1, 2]$ and $M = 3$, then $B = A*M = [1, 2, 1, 2, 1, 2]$

You have to help him to find out the minimum value of $M$ such that the length of the **longest strictly increasing subsequence** is maximum possible.

###Input:
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

###Output:
For each test case, print a single line containing one integer ― the **minimum** value of $M$.

###Constraints 
- $1 \le T \le 500$
- $1 \le N \le 2*10^5$
- $1 \le A_i \le 10^9$
- It's guaranteed that the total length of the sequence $A$ in one test file doesn't exceed $2*10^6$

###Sample Input:
```
3
2
2 1
2
1 2
5
1 3 2 1 2
```

###Sample Output:
```
2
1
2
```

### Explanation:
In the first test case, Choosing $M = 2$ gives $B = [2, 1, 2, 1]$ which has a longest strictly increasing sequence of length $2$ which is the maximum possible.

In the second test case, Choosing $M = 1$ gives $B  = [1, 2]$ which has a longest strictly increasing sequence of length $2$ which is the maximum possible.

<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>