There are N children standing in a line. Each child is assigned a rating value.

You are giving candies to these children subjected to the following requirements:


       Each child must have at least one candy.
       Children with a higher rating get more candies than their neighbors.


What is the minimum candies you must give?

Example 1:


Input: [1,0,2]
Output: 5
Explanation: You can allocate to the first, second and third child with 2, 1, 2 candies respectively.


Example 2:


Input: [1,2,2]
Output: 4
Explanation: You can allocate to the first, second and third child with 1, 2, 1 candies respectively.
             The third child gets 1 candy because it satisfies the above two conditions.

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class Solution:\n     def candy(self, ratings):\n         """\n         :type ratings: List[int]\n         :rtype: int\n         """\n         candies = [0] * len(ratings)\n         # min candies at idx i = max of\n         # 1) (number of decreasing ratings to the left) + 1\n         # 2) (number of decreasing ratings to the right) + 1\n         # By definition number after end of decreasing sequence will be greater than the end\n         # => both sides of end of decreasing sequence will be greater than the rating at the end\n         # => the min number of candies at the end of the decreasing sequence is 1\n         # => min number of candies at the (end-n) of the decreasing sequence is 1+n        \n         from_left = [1] * len(ratings)\n         cur_less_than = 1\n         for idx in range(1, len(ratings)):\n             if ratings[idx-1] < ratings[idx]:\n                 cur_less_than += 1\n             else:\n                 cur_less_than = 1\n             from_left[idx] = cur_less_than\n         \n         from_right = [1] * len(ratings)\n         cur_less_than = 1\n         idx = len(ratings)-2\n         while idx >= 0:\n             if ratings[idx+1] < ratings[idx]:\n                 cur_less_than += 1\n             else:\n                 cur_less_than = 1\n             from_right[idx] = cur_less_than\n             idx -= 1\n             \n         for idx in range(0, len(ratings)):\n             candies[idx] = max(from_left[idx], from_right[idx])\n             \n         return sum(candies)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'candy'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5978