luckybal
Problem Description
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 i^th 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.
Contest Information
- Contest ID: 0
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- Points: 0.0
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- Time Limit: None seconds
- Memory Limit: 0 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.