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 (x-1)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

----- Sample Input 1 ------ 
2
47
4477
----- Sample Output 1 ------ 
1
4

Source: codechef | Difficulty: HARD
Tags: Matrices

Combinatorics

Mathematics


Solutions:
mod = 1000000007
fact = [1]
for i in range(1, 5003):
	fact.append(i * fact[i - 1] % mod)
inv = []
for j in range(5003):
	nv = pow(fact[j], mod - 2, mod)
	inv.append(nv)
for j in range(int(input())):
	l = input()
	four = l.count('4')
	seven = l.count('7')
	if four == 0 or seven == 0:
		print(1)
	else:
		ans = fact[len(l)] * inv[four] * inv[len(l) - four] % mod
		ans = (ans - fact[len(l) - 2] * inv[four - 1] * inv[len(l) - 1 - four]) % mod
		print(ans % mod)