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 = 'def findM(A, n):\r\n    elemIdxMap = dict()\r\n    for i in range(n):\r\n        if A[i] in elemIdxMap:\r\n            elemIdxMap[A[i]].append(i)\r\n        else:\r\n            elemIdxMap[A[i]] = [i]\r\n    \r\n    keys = sorted(elemIdxMap.keys())\r\n    \r\n    # print(elemIdxMap, keys)\r\n\r\n    connected = False\r\n    count = 0\r\n    prevIdx = -1\r\n\r\n    nKeys = len(keys)\r\n    for i in range(nKeys-1):\r\n        \r\n        if not connected:\r\n            prevIdx = elemIdxMap[keys[i]][0]\r\n            \r\n            for idx in elemIdxMap[keys[i+1]]:\r\n                if idx >prevIdx:\r\n                    connected = True\r\n                    count += 1\r\n                    prevIdx = idx\r\n                    break\r\n        else:\r\n            connected = False\r\n\r\n            for idx in elemIdxMap[keys[i+1]]:\r\n                if idx > prevIdx:\r\n                    connected = True\r\n                    count += 1\r\n                    prevIdx = idx\r\n                    break\r\n\r\n        # print(keys[i], count, prevIdx)\r\n    # if count == nKeys - 1:\r\n    #     return 1\r\n    # else:\r\n    #     return (nKeys - count)\r\n    # print(nKeys, count)\r\n    return (nKeys - count)\r\n\r\n\r\ndef __starting_point():\r\n    for _ in range(int(input())):\r\n        n = int(input())\r\n        A = list(map(int, input().split()))\r\n        \r\n        print(findM(A, n))\r\n        # print(findM([1, 3, 2, 1, 2], 5))\r\n        \r\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13583