#include <bits/stdc++.h>
using namespace std;

#define ll long long
const int M = 1e9+7;
const int N = 1e7+5;

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        string s;
        cin >> s;
        string p;
        for(auto c:s){
            if(c=='(') p+='l';
            else p+='r';
        }
        vector<int> suf(n);
        int cnt = 0;
        for (int i = n-1; i >=0; --i)
        {
            if(p[i]=='r'){
                cnt++;
            }
            suf[i]=cnt;
        }
        std::vector<int> lPos;
        for (int i = 0; i < n; ++i)
        {
            if(p[i]=='l') lPos.push_back(i);
        }
        int lCnt = 0, mainCnt=0;
        int maxi = INT_MIN;
        for (int i = 0; i < n; ++i)
        {
            if(p[i]=='l'){
                lCnt++;
                mainCnt++;
            }
            else {
                int l_position = lPos[mainCnt-1]+1;
                if(l_position<n){
                    int r_cnt = suf[l_position];
                    if(r_cnt>=lCnt){
                        maxi = max(maxi , 2*lCnt);
                    }
                    else lCnt--;
                }
            }
        }
        if(maxi==INT_MIN){
            cout << -1 << '\n';
        }
        else cout << maxi << "\n";
    }
    return 0;
}