In ChefLand, there is a mountain range consisting of $N$ hills (numbered $1$ through $N$) in a straight line. Let's denote the height of the $i$-th hill from the left by $h_i$.
Ada is working on the water supply system of ChefLand. On some of the hills, she wants to place water reservoirs; then, for each reservoir, she will decide in which direction the water should flow from it — either to the left or to the right (water may not flow in both directions from the same reservoir). From a reservoir on a hill with height $h$, water flows in the chosen direction until it reaches the first hill that is strictly higher than $h$; all hills before this hill (including the hill containing the reservoir) are therefore supplied with water.
For example, suppose we have hills with heights $[7, 2, 3, 5, 8]$. If we place a reservoir on the hill with height $5$, and pump water from it to the left, then the hills with heights $2$, $3$ and $5$ are supplied with water.
Help Ada find the minimum numer of reservoirs needed to provide water to all the hills if she chooses the directions optimally.

-----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 $h_1, h_2, \dots, h_N$.

-----Output-----
For each test case, print a single line containing one integer — the minimum required number of reservoirs.

-----Constraints-----
- $2 \le N \le 10^5$
- $1 \le h_i \le 10^9$ for each valid $i$
- $h_i \neq h_j $ for any valid $i \neq j$
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$

-----Example Input-----
1
6
4 16 32 6 8 2

-----Example Output-----
2    

-----Explanation-----
Example case 1: We can place reservoirs on the second and third hill, pumping water to the left and right respectively.

```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 = 'for i in range(int(input())):\n    n=int(input())\n    count = 0\n    hill = list(map(int, input().split()))\n    def res(hills):\n        maxval = max(hills)\n        maxpos = hills.index(maxval)\n        \n        left=list()\n        right=list()\n        \n        if maxpos is 0 or maxpos is len(hills)-1 :\n            return 1\n        \n        for j in range(maxpos):\n            left.append(hills[j])\n        for j in range(maxpos+1,len(hills)):\n            right.append(hills[j])\n        \n        return 1+min(res(right),res(left))\n    \n    print(res(hill))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12983