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 = int(input())
skobs = input()
cnt9 = 0
fl = 0
cnt0 = 0
cnt10, cnt19 = 0, 0
bz = float("inf")
bz2 = float("-inf")
for y in range(n):
    if skobs[y] == "(":
        cnt9 += 1
    else:
        cnt0 += 1
    if cnt0 - cnt9 > 2:
        fl = 1
    if cnt0 - cnt9 == 1:
        bz = min(bz, y)
for y2 in range(n-1, -1, -1):
    if skobs[y2] == "(":
        cnt19 += 1
    else:
        cnt10 += 1
    if cnt19 - cnt10 > 2:
        fl = 1
    if cnt19 - cnt10 == 1:
        bz2 = max(bz2, y2)
if abs(cnt9-cnt0) != 2 or fl or (bz2 != float("-inf") and bz != float("inf")):
    print(0)
elif bz == float("inf") and bz2 != float("-inf"):
    ww = skobs[bz2:]
    print(ww.count("("))
elif bz2 == float("-inf") and bz != float("inf"):
    ww = skobs[:bz+1]
    print(ww.count(")"))



