Lucky Balance

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Chef has the string s of length n consisted of digits 4 and 7.
The string s is called balanced
if there exits such integer x (1 ≤ x ≤ n) that the number of digits 4 in substring s[1; x) is equal to the number of digits 7 in substring s(x; n],
where s[1; x) is the substring from the 1st digit to (x1)th digit of s, and s(x; n] is the substring from the (x+1)th digit to nth digit of s.
For example, s = 747474 is a balanced string, because s[1; 4) = 747 has one 4 and s(4; 6] = 74 has one 7.
Note that x can be 1 or n and s[1; 1) and s(n; n] denote an empty string.
In one turn Chef can choose any pair of consecutive digits and swap them.
Find for Chef the total number of different balanced string that can be obtained from string s using any (even 0) number of turns.
Print the result modulo 1000000007.
Input
The first line of the input contains one integer T, the number of test cases.
Then T lines follow, each of which contains string s for the corresponding test.
Output
T lines, each of which contains single integer  the answer for the corresponding test modulo 10^{9}+7.
Constraints
1 ≤ T ≤ 10
1 ≤ n ≤ 5000
Example
Input: 2 47 4477 Output: 1 4
Author:  witua 
Tester:  laycurse 
Editorial  http://discuss.codechef.com/problems/LUCKY9 
Tags  binomial, maths, medium, nov12, witua 
Date Added:  15022012 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS 
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