Sereja has a bracket sequence s1, s2, ..., sn, or, in other words, a string s of length n, consisting of characters "(" and ")".

Sereja needs to answer m queries, each of them is described by two integers li, ri (1 ≤ li ≤ ri ≤ n). The answer to the i-th query is the length of the maximum correct bracket subsequence of sequence sli, sli + 1, ..., sri. Help Sereja answer all queries.

You can find the definitions for a subsequence and a correct bracket sequence in the notes.

Input

The first line contains a sequence of characters s1, s2, ..., sn (1 ≤ n ≤ 106) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1 ≤ m ≤ 105) — the number of queries. Each of the next m lines contains a pair of integers. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n) — the description of the i-th query.

Output

Print the answer to each question on a single line. Print the answers in the order they go in the input.

Examples

Input

())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10


Output

0
0
2
10
4
6
6

Note

A subsequence of length |x| of string s = s1s2... s|s| (where |s| is the length of string s) is string x = sk1sk2... sk|x| (1 ≤ k1 < k2 < ... < k|x| ≤ |s|).

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

For the third query required sequence will be «()».

For the fourth query required sequence will be «()(())(())».
import sys
import math
input=sys.stdin.readline
s=input().rstrip()
n=len(s)
q=int(input())
class segTree:
    def __init__(self):
        self.a=[0]*(2*n)
        self.b=[0]*(2*n)
        self.c=[0]*(2*n)
    def build(self,arr):
        for i in range(n):
            self.a[i+n]=0
            self.b[i+n]=1 if arr[i]=="(" else 0
            self.c[i+n]=1 if arr[i]==")" else 0
        for i in range(n-1,0,-1):
            t=min(self.b[i<<1],self.c[i<<1|1])
            self.a[i]=self.a[i<<1]+self.a[i<<1|1]+2*t
            self.b[i]=self.b[i<<1]+self.b[i<<1|1]-t
            self.c[i]=self.c[i<<1]+self.c[i<<1|1]-t
    def query(self,l,r):
        left=[]
        right=[]
        l+=n
        r+=n
        while l<=r:
            if (l&1):
                left.append([self.a[l],self.b[l],self.c[l]])
                l+=1
            if not (r&1):
                right.append([self.a[r],self.b[r],self.c[r]])
                r-=1
            l>>=1
            r>>=1
        a1=b1=c1=0
        for a2,b2,c2 in left+right[::-1]:
            t=min(b1,c2)
            a1+=a2+2*t
            b1+=b2-t
            c1+=c2-t
        return a1
tr=segTree()
tr.build(s)
for _ in range(q):
    l,r=map(int,input().split())
    print(tr.query(l-1,r-1))