#include <bits/stdc++.h>
using namespace std;
long long int gcd(long long int a, long long int b) {
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}
long long int lcm(long long int a, long long int b) {
  return (a / gcd(a, b)) * b;
}
long long int ncr(long long int n, long long int r) {
  long long int p = 1, k = 1;
  if (n - r < r) r = n - r;
  if (r != 0) {
    while (r) {
      p *= n % 1000000007;
      k *= r % 1000000007;
      long long int m = gcd(p, k);
      p /= m;
      k /= m;
      n--;
      r--;
    }
  } else
    p = 1;
  return p % 1000000007;
}
long long int mod_exp(long long int a, long long int b, long long int m) {
  a %= m;
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % m;
    a = a * a % m;
    b = b / 2;
  }
  return res;
}
long long int get_div(long long int n) {
  long long int sum = 0;
  for (long long int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        sum += i;
      else {
        sum += i;
        sum += (n / i);
      }
    }
  }
  return sum;
}
bool isPrime(long long int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (long long int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
vector<long long int> SieveOfEratosthenes(long long int n) {
  vector<long long int> arr(n + 1, 0);
  bool prime[n + 1];
  memset(prime, true, sizeof(prime));
  for (long long int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (long long int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
  for (long long int j = 2; j <= n; j++) {
    arr[j] = arr[j - 1];
    if (prime[j]) arr[j]++;
  }
  return arr;
}
long long int primeFactors(long long int n, long long int k) {
  if (isPrime(n)) return 1;
  long long int c = 0;
  while (n % 2 == 0) {
    c++;
    n = n / 2;
  }
  for (long long int i = 3; i <= sqrt(n) + 1; i = i + 2) {
    while (n % i == 0) {
      c++;
      n = n / i;
    }
  }
  if (n > 2) {
    c++;
  }
  return c;
}
bool isp(string s) {
  for (long long int i = 0; i < (s.size() / 2); i++) {
    if (s[i] != s[s.size() - 1 - i]) return false;
  }
  return true;
}
long long int len(long long int n) {
  long long int ans = 0;
  while (n != 0) {
    n = n / 10;
    ans++;
  }
  return ans;
}
long long int binarySearch(long long int p, long long int r, long long int n) {
  if (p <= r) {
    long long int mid = (p + r) / 2;
    if (mid == n) {
      return mid;
    } else if (mid > n)
      return binarySearch(p, mid - 1, n);
    else if (mid < n)
      return binarySearch(mid + 1, r, n);
  }
  return -1;
}
void divisors_till_n(int n) {
  long long int divisors[100000];
  for (int i = 1; i <= n; i++) {
    for (int j = i; j <= n; j += i) {
      divisors[j]++;
      divisors[j] %= 998244353;
    }
  }
}
long long int countFreq(string &pat, string &txt) {
  long long int M = pat.length();
  long long int N = txt.length();
  long long int res = 0;
  for (int i = 0; i <= N - M; i++) {
    int j;
    for (j = 0; j < M; j++)
      if (txt[i + j] != pat[j]) break;
    if (j == M) {
      res++;
      j = 0;
    }
  }
  return res;
}
vector<int> z_function(string s) {
  int n = (int)s.length();
  vector<int> z(n);
  for (int i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) z[i] = min(r - i + 1, z[i - l]);
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) ++z[i];
    if (i + z[i] - 1 > r) l = i, r = i + z[i] - 1;
  }
  return z;
}
bool sortbysecdesc(const pair<long long int, long long int> &a,
                   const pair<long long int, long long int> &b) {
  return a.second < b.second;
}
long long int close(long long int n, long long int a, long long int b) {
  long long int div = n / b;
  long long int no = n / a;
  while ((n - (div)*b) % a != 0 && div >= (n - (a * no))) div--;
  if (div >= 0) return div;
  return -1;
}
long long int op(long long int num1, long long int num2) {
  long long int ans = 0;
  long long int p = 0;
  while (num1 != 0) {
    long long int bin1, bin2;
    bin1 = num1 % 2;
    bin2 = num2 % 2;
    if (bin1 == 1 && bin2 == 0) {
      ans += pow(2, p);
    }
    p++;
    num1 = num1 / 2;
    num2 = num2 / 2;
  }
  return ans;
}
long long int func(long long int n) {
  long long int p = 0, ans = 0;
  while (n != 0) {
    long long int num = n % 10;
    if (num >= 1) {
      ans += pow(10, p);
    }
    p++;
    n = n / 10;
  }
  return ans;
}
struct cust {
  double val;
  long long int ii;
  long long int jj;
};
bool operator<(const cust &c1, const cust &c2) { return c1.val < c2.val; }
long long int solve(string n, vector<long long int> p) {
  long long int ans = 1e10;
  for (long long int i = 0; i < p.size(); i++) {
    long long int f = 0;
    string s = to_string(p[i]);
    long long int j = 0;
    for (long long int k = 0; k < n.size() && j < s.size(); k++) {
      if (s[j] == n[k]) {
        j++;
      }
    }
    long long int moves = (n.size() - j) + (s.size() - j);
    ans = min(moves, ans);
  }
  return ans;
}
long long int voting_algo(vector<vector<long long int>> arr, long long int n) {
  long long int count1 = 0, count2 = 0;
  long long int first = 0, second = 1;
  for (long long int j = 0; j < arr[0].size(); j++) {
    for (long long int i = 0; i < n; i++) {
      if (arr[first][j] >= arr[i][j] && count1 != 0)
        count1++;
      else if (arr[second][j] >= arr[i][j] && count2 != 0)
        count2++;
      else if (count1 == 0) {
        count1++;
        first = i + 1;
      } else if (count2 == 0) {
        count2++;
        second = i + 1;
      } else {
        count1--;
        count2--;
      }
    }
  }
  count1 = 0;
  count2 = 0;
  for (long long int j = 0; j < arr[0].size(); j++) {
    for (long long int i = 0; i < n; i++) {
      if (arr[first][j] >= arr[i][j])
        count1++;
      else if (arr[second][j] >= arr[i][j])
        count2++;
    }
  }
  if (count1 > n / 3) return first;
  if (count2 > n / 3) return second;
  return -1;
}
int main() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    string brk = "()";
    for (long long int i = n; i >= 1; i--) {
      string ans{""};
      for (long long int j = i; j >= 1; j--) ans += brk;
      for (long long int j = n - i; j >= 1; j--) ans += ")";
      for (long long int j = n - i; j >= 1; j--) ans = "(" + ans;
      cout << ans << endl;
    }
  }
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

A bracket sequence is a string containing only characters "(" and ")". 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 "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.

You are given an integer n. Your goal is to construct and print exactly n different regular bracket sequences of length 2n.

Input

The first line contains one integer t (1 ≤ t ≤ 50) — the number of test cases.

Each test case consists of one line containing one integer n (1 ≤ n ≤ 50).

Output

For each test case, print n lines, each containing a regular bracket sequence of length exactly 2n. All bracket sequences you output for a testcase should be different (though they may repeat in different test cases). If there are multiple answers, print any of them. It can be shown that it's always possible.

Example

Input


3
3
1
3


Output


()()()
((()))
(()())
()
((()))
(())()
()(())

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long int gcd(long long int a, long long int b) {
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}
long long int lcm(long long int a, long long int b) {
  return (a / gcd(a, b)) * b;
}
long long int ncr(long long int n, long long int r) {
  long long int p = 1, k = 1;
  if (n - r < r) r = n - r;
  if (r != 0) {
    while (r) {
      p *= n % 1000000007;
      k *= r % 1000000007;
      long long int m = gcd(p, k);
      p /= m;
      k /= m;
      n--;
      r--;
    }
  } else
    p = 1;
  return p % 1000000007;
}
long long int mod_exp(long long int a, long long int b, long long int m) {
  a %= m;
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % m;
    a = a * a % m;
    b = b / 2;
  }
  return res;
}
long long int get_div(long long int n) {
  long long int sum = 0;
  for (long long int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        sum += i;
      else {
        sum += i;
        sum += (n / i);
      }
    }
  }
  return sum;
}
bool isPrime(long long int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (long long int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
vector<long long int> SieveOfEratosthenes(long long int n) {
  vector<long long int> arr(n + 1, 0);
  bool prime[n + 1];
  memset(prime, true, sizeof(prime));
  for (long long int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (long long int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
  for (long long int j = 2; j <= n; j++) {
    arr[j] = arr[j - 1];
    if (prime[j]) arr[j]++;
  }
  return arr;
}
long long int primeFactors(long long int n, long long int k) {
  if (isPrime(n)) return 1;
  long long int c = 0;
  while (n % 2 == 0) {
    c++;
    n = n / 2;
  }
  for (long long int i = 3; i <= sqrt(n) + 1; i = i + 2) {
    while (n % i == 0) {
      c++;
      n = n / i;
    }
  }
  if (n > 2) {
    c++;
  }
  return c;
}
bool isp(string s) {
  for (long long int i = 0; i < (s.size() / 2); i++) {
    if (s[i] != s[s.size() - 1 - i]) return false;
  }
  return true;
}
long long int len(long long int n) {
  long long int ans = 0;
  while (n != 0) {
    n = n / 10;
    ans++;
  }
  return ans;
}
long long int binarySearch(long long int p, long long int r, long long int n) {
  if (p <= r) {
    long long int mid = (p + r) / 2;
    if (mid == n) {
      return mid;
    } else if (mid > n)
      return binarySearch(p, mid - 1, n);
    else if (mid < n)
      return binarySearch(mid + 1, r, n);
  }
  return -1;
}
void divisors_till_n(int n) {
  long long int divisors[100000];
  for (int i = 1; i <= n; i++) {
    for (int j = i; j <= n; j += i) {
      divisors[j]++;
      divisors[j] %= 998244353;
    }
  }
}
long long int countFreq(string &pat, string &txt) {
  long long int M = pat.length();
  long long int N = txt.length();
  long long int res = 0;
  for (int i = 0; i <= N - M; i++) {
    int j;
    for (j = 0; j < M; j++)
      if (txt[i + j] != pat[j]) break;
    if (j == M) {
      res++;
      j = 0;
    }
  }
  return res;
}
vector<int> z_function(string s) {
  int n = (int)s.length();
  vector<int> z(n);
  for (int i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) z[i] = min(r - i + 1, z[i - l]);
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) ++z[i];
    if (i + z[i] - 1 > r) l = i, r = i + z[i] - 1;
  }
  return z;
}
bool sortbysecdesc(const pair<long long int, long long int> &a,
                   const pair<long long int, long long int> &b) {
  return a.second < b.second;
}
long long int close(long long int n, long long int a, long long int b) {
  long long int div = n / b;
  long long int no = n / a;
  while ((n - (div)*b) % a != 0 && div >= (n - (a * no))) div--;
  if (div >= 0) return div;
  return -1;
}
long long int op(long long int num1, long long int num2) {
  long long int ans = 0;
  long long int p = 0;
  while (num1 != 0) {
    long long int bin1, bin2;
    bin1 = num1 % 2;
    bin2 = num2 % 2;
    if (bin1 == 1 && bin2 == 0) {
      ans += pow(2, p);
    }
    p++;
    num1 = num1 / 2;
    num2 = num2 / 2;
  }
  return ans;
}
long long int func(long long int n) {
  long long int p = 0, ans = 0;
  while (n != 0) {
    long long int num = n % 10;
    if (num >= 1) {
      ans += pow(10, p);
    }
    p++;
    n = n / 10;
  }
  return ans;
}
struct cust {
  double val;
  long long int ii;
  long long int jj;
};
bool operator<(const cust &c1, const cust &c2) { return c1.val < c2.val; }
long long int solve(string n, vector<long long int> p) {
  long long int ans = 1e10;
  for (long long int i = 0; i < p.size(); i++) {
    long long int f = 0;
    string s = to_string(p[i]);
    long long int j = 0;
    for (long long int k = 0; k < n.size() && j < s.size(); k++) {
      if (s[j] == n[k]) {
        j++;
      }
    }
    long long int moves = (n.size() - j) + (s.size() - j);
    ans = min(moves, ans);
  }
  return ans;
}
long long int voting_algo(vector<vector<long long int>> arr, long long int n) {
  long long int count1 = 0, count2 = 0;
  long long int first = 0, second = 1;
  for (long long int j = 0; j < arr[0].size(); j++) {
    for (long long int i = 0; i < n; i++) {
      if (arr[first][j] >= arr[i][j] && count1 != 0)
        count1++;
      else if (arr[second][j] >= arr[i][j] && count2 != 0)
        count2++;
      else if (count1 == 0) {
        count1++;
        first = i + 1;
      } else if (count2 == 0) {
        count2++;
        second = i + 1;
      } else {
        count1--;
        count2--;
      }
    }
  }
  count1 = 0;
  count2 = 0;
  for (long long int j = 0; j < arr[0].size(); j++) {
    for (long long int i = 0; i < n; i++) {
      if (arr[first][j] >= arr[i][j])
        count1++;
      else if (arr[second][j] >= arr[i][j])
        count2++;
    }
  }
  if (count1 > n / 3) return first;
  if (count2 > n / 3) return second;
  return -1;
}
int main() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    string brk = "()";
    for (long long int i = n; i >= 1; i--) {
      string ans{""};
      for (long long int j = i; j >= 1; j--) ans += brk;
      for (long long int j = n - i; j >= 1; j--) ans += ")";
      for (long long int j = n - i; j >= 1; j--) ans = "(" + ans;
      cout << ans << endl;
    }
  }
}

```