| # luckybal |
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| ## 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. |
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| Let S be some lucky string. Then |
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| |S| denotes the length of the string S; |
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| S[i] (1 ≤ i ≤ |S|) denotes the i^th character of S (the numeration of characters starts from 1); |
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| 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. |
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| 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. |
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| Output |
| For each test case output a single line containing the answer for this test case. |
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| Constraints |
| 1 ≤ T ≤ 10 |
| 1 ≤ |S| ≤ 100000 |
| S consists only of the lucky digits 4 and 7. |
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| Example |
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| Input: |
| 4 |
| 47 |
| 74 |
| 477 |
| 4747477 |
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| Output: |
| 2 |
| 2 |
| 3 |
| 23 |
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| 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. |
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| ## Contest Information |
| - **Contest ID**: 0 |
| - **Problem Index**: |
| - **Points**: 0.0 |
| - **Rating**: 0 |
| - **Tags**: None |
| - **Time Limit**: None seconds |
| - **Memory Limit**: 0 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
