Zookeeper is buying a carton of fruit to feed his pet wabbit. The fruits are a sequence of apples and oranges, which is represented by a binary string $s_1s_2\ldots s_n$ of length $n$. $1$ represents an apple and $0$ represents an orange.

Since wabbit is allergic to eating oranges, Zookeeper would like to find the longest contiguous sequence of apples. Let $f(l,r)$ be the longest contiguous sequence of apples in the substring $s_{l}s_{l+1}\ldots s_{r}$. 

Help Zookeeper find $\sum_{l=1}^{n} \sum_{r=l}^{n} f(l,r)$, or the sum of $f$ across all substrings.


-----Input-----

The first line contains a single integer $n$ $(1 \leq n \leq 5 \cdot 10^5)$.

 The next line contains a binary string $s$ of length $n$ $(s_i \in \{0,1\})$ 


-----Output-----

Print a single integer: $\sum_{l=1}^{n} \sum_{r=l}^{n} f(l,r)$. 


-----Examples-----
Input
4
0110

Output
12

Input
7
1101001

Output
30

Input
12
011100011100

Output
156



-----Note-----

In the first test, there are ten substrings. The list of them (we let $[l,r]$ be the substring $s_l s_{l+1} \ldots s_r$):  $[1,1]$: 0  $[1,2]$: 01  $[1,3]$: 011  $[1,4]$: 0110  $[2,2]$: 1  $[2,3]$: 11  $[2,4]$: 110  $[3,3]$: 1  $[3,4]$: 10  $[4,4]$: 0 

The lengths of the longest contiguous sequence of ones in each of these ten substrings are $0,1,2,2,1,2,2,1,1,0$ respectively. Hence, the answer is $0+1+2+2+1+2+2+1+1+0 = 12$.

```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 = 'n = int(input())\na = list(map(int, input()))\n\nacc = 0\nback = 0\ntop = 0\ncur = 0\ns = []\n\nfor i,x in enumerate(a):\n\tif x == 0:\n\t\tcur = 0\n\telse:\n\t\tif cur > 0:\n\t\t\ts.pop()\n\t\tcur += 1\n\t\tif cur >= top:\n\t\t\ttop = cur\n\t\t\tback = (cur + 1) * (cur) // 2 + (i - cur + 1) * cur\n\t\t\ts = [(cur, i)]\n\t\telse:\n\t\t\tback += i - (s[-1][1] - cur + 1)\n\t\t\tif cur >= s[-1][0]:\n\t\t\t\ts.pop()\n\t\t\ts += [(cur, i)]\n\tacc += back\n\t#print(i,x,acc, back, top, cur)\n\t#print(s)\n\n\nprint(acc)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13211