You are given a bracket sequence s consisting of n opening '(' and closing ')' brackets.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You can change the type of some bracket s_i. It means that if s_i =  ')' then you can change it to '(' and vice versa.

Your task is to calculate the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 10^6) — the length of the bracket sequence.

The second line of the input contains the string s consisting of n opening '(' and closing ')' brackets.

Output

Print one integer — the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Examples

Input


6
(((())


Output


3


Input


6
()()()


Output


0


Input


1
)


Output


0


Input


8
)))(((((


Output


0
n = input()
s = raw_input()
arr = []
for i in range(n):
    if s[i] == "(":
        arr.append(1)
    else:
        arr.append(-1)
psum = [0]*(1+n)
for i in range(n):
    psum[i+1] = arr[i]+psum[i]

if sum(arr) == 2:
    if min(psum)<0:
        print 0
    else:
        cnt = 0
        for i in range(n)[::-1]:
            if psum[i+1] < 2:
                break
            if arr[i] == 1:
                cnt += 1
        print cnt
elif sum(arr) == -2:
    if min(psum)<-2:
        print 0
    else:
        cnt = 0
        for i in range(n):
            if arr[i] == -1:
                cnt += 1
            if psum[i+1] <= -1:
                break
        print cnt
else:
    print 0
		    		  		 	  				   	 	 		