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
input()
line = input()
wasm = -1
last0 = 0
last1 = -1
curs = 0
err = False
for i in range(len(line)):
    if line[i]=='(':
        curs+=1
    else:
        curs-=1
    if curs == 0:
        last0=i
    if curs == 1:
        last1=i
    if curs < 0:
        if wasm == -1:
            wasm=i
        if curs < -2:
            err = True
            break
if err:
    print(0)
elif wasm == -1:
    if curs != 2:
        print(0)
    else:
        print(int((len(line)-max(last0,last1))/2))
else:
    if curs != -2:
        print(0)
    else:
        print(int(wasm/2) + 1)