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.

Starter code:

Solutions:
x=eval(input())
for x in range(0,x):
	ans=0
	d=input()
	a=0
	cont=0
	for i in range(0,len(d)):
		a+=len(d)-i
		if d[i]=='7':
			ans+=1+cont
			cont+=1
		else:
			cont=0
	ans=a-ans
	print(ans)


for _ in range(int(input())):
	s = input()
	a = s.split('4')
	sum1 = 0
	for k in a:
		sum1 = sum1 + (len(k)*(len(k)+1))/2
	l = len(s) *(len(s)+1) / 2
	print(l - sum1)

#import psyco
#psyco.full()

for _ in range(int(input())):
    s=input().strip()
    ways=0
    l=len(s)
    
    index=[]
    for i in range(l):
        if s[i]=='4':
            index.append(i)
    if len(index)==0:
        print(0)
    else:
        ways=0
        ways+=(index[0]+1-0)*(l-index[0])
        for i in range(1,len(index)):
            ways+=(index[i]-index[i-1])*(l-index[i])
                
        print(ways)

tcase=int(eval(input()))
i=0
while(tcase):
    tcase-=1
    a=str(input())
    j=0
    i=0
    rem=0
    length=len(a)
    ans=(length*(length+1))/2
    #print ans,
    while(i<length):
        if(a[i]=='7'):
            rem+=(i-j+1)
            #print i,j,
        else:
            j=i+1
        i+=1
    ans-= rem;
    print(ans);



#import psyco
#psyco.full()

for _ in range(int(input())):
    s=input().strip()
    ways=0
    l=len(s)
    
    index=[]
    for i in range(l):
        if s[i]=='4':
            index.append(i)
    ways=0        
    for i in range(len(index)):
        if i==0:
            ways+=(index[i]+1-0)*(l-index[i])
        else:
            ways+=(index[i]-index[i-1])*(l-index[i])
            
    print(ways)

t=int(input().strip())
for i in range(t):
    word=input().strip()
    n=len(word)
    s=n*(n+1)/2
    t7=0
    for j in range(n):
        if word[j]=='7': t7+=1
        else:
            s-=t7*(t7+1)/2
            t7=0
    s-=t7*(t7+1)/2
    print(s)
    


t=int(input().strip())
for i in range(t):
    word=input().strip()
    n=len(word)
    s=n*(n+1)/2
    t7=0
    for j in range(n):
        if word[j]=='7': t7+=1
        else:
            s-=t7*(t7+1)/2
            t7=0
    s-=t7*(t7+1)/2
    print(s)