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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 't = int(input())\r\nfor _ in range(t):\r\n    n = int(input())\r\n    a = [int(x) for x in input().strip().split()]\r\n    a = [(a[i],i) for i in range(n)]\r\n    a.sort()\r\n    res=1\r\n    prev=0\r\n    prev_ind = -1\r\n  \r\n    i=0\r\n    while i<n:\r\n        if a[i][1]>prev_ind:\r\n            prev_ind = a[i][1]\r\n            prev = a[i][0]\r\n            while i<n and a[i][0]==prev:\r\n                i+=1\r\n        else:\r\n            prev = a[i][0]\r\n            flag = False\r\n            mn=a[i][1]\r\n            while i<n and a[i][0]==prev:\r\n                if a[i][1]>prev_ind:\r\n                    prev_ind=a[i][1]\r\n                    flag = True\r\n                    break\r\n                i+=1\r\n            if flag:\r\n                while i<n and a[i][0]==prev:\r\n                    i+=1\r\n            else:\r\n                res+=1\r\n                prev_ind=mn\r\n    print(res)\r\n\r\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13645