A Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7.
The Little Elephant calls some string T of the length M balanced if there exists at least one integer X (1 ≤ X ≤ M) such that the number of digits 4 in the substring T[1, X - 1] is equal to the number of digits 7 in the substring T[X, M]. For example, the string S = 7477447 is balanced since S[1, 4] = 7477 has 1 digit 4 and S[5, 7] = 447 has 1 digit 7. On the other hand, one can verify that the string S = 7 is not balanced.
The Little Elephant has the string S of the length N. He wants to know the number of such pairs of integers (L; R) that 1 ≤ L ≤ R ≤ N and the substring S[L, R]  is balanced. Help him to find this number.
Notes.

Let S be some lucky string. Then

- |S| denotes the length of the string S;

- S[i] (1 ≤ i ≤ |S|) denotes the ith character of S (the numeration of characters starts from 1);

-  S[L, R] (1 ≤ L ≤ R ≤ |S|) denotes the string with the following sequence of characters: S[L], S[L + 1], ..., S[R], and is called a substring of S. For L > R we mean by S[L, R] an empty string.

-----Input-----
The first line of the input file contains a single integer T, the number of test cases. Each of the following T lines contains one string, the string S for the corresponding test case. The input file does not contain any whitespaces.

-----Output-----
For each test case output a single line containing the answer for this test case.

-----Constraints-----
1 ≤ T ≤ 10

1 ≤ |S| ≤ 100000

S consists only of the lucky digits 4 and 7.


-----Example-----
Input:
4
47
74
477
4747477

Output:
2
2
3
23

-----Explanation-----

In the first test case balance substrings are S[1, 1] = 4 and S[1, 2] = 47.
In the second test case balance substrings are S[2, 2] = 4 and S[1, 2] = 74.
Unfortunately, we can't provide you with the explanations of the third and the fourth test cases. You should figure it out by yourself. Please, don't ask about this in comments.

```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 _ in range(int(input())):\n\ts = input()\n\ta = s.split('4')\n\tsum1 = 0\n\tfor k in a:\n\t\tsum1 = sum1 + (len(k)*(len(k)+1))/2\n\tl = len(s) *(len(s)+1) / 2\n\tprint(l - sum1)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13019