On the competitive programming platform CodeCook, every person has a rating graph described by an array of integers a of length n. You are now updating the infrastructure, so you've created a program to compress these graphs.

The program works as follows. Given an integer parameter k, the program takes the minimum of each contiguous subarray of length k in a.

More formally, for an array a of length n and an integer k, define the k-compression array of a as an array b of length n-k+1, such that $$$b_j =min_{j≤ i≤ j+k-1}a_i$$$

For example, the 3-compression array of [1, 3, 4, 5, 2] is [min\{1, 3, 4\}, min\{3, 4, 5\}, min\{4, 5, 2\}]=[1, 3, 2].

A permutation of length m is an array consisting of m distinct integers from 1 to m in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (m=3 but there is 4 in the array).

A k-compression array will make CodeCook users happy if it will be a permutation. Given an array a, determine for all 1≤ k≤ n if CodeCook users will be happy after a k-compression of this array or not.

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of the description of each test case contains a single integer n (1≤ n≤ 3⋅ 10^5) — the length of the array.

The second line of the description of each test case contains n integers a_1,…,a_n (1≤ a_i≤ n) — the elements of the array.

It is guaranteed, that the sum of n for all test cases does not exceed 3⋅ 10^5.

Output

For each test case, print a binary string of length n. 

The k-th character of the string should be 1 if CodeCook users will be happy after a k-compression of the array a, and 0 otherwise. 

Example

Input


5
5
1 5 3 4 2
4
1 3 2 1
5
1 3 3 3 2
10
1 2 3 4 5 6 7 8 9 10
3
3 3 2


Output


10111
0001
00111
1111111111
000

Note

In the first test case, a=[1, 5, 3, 4, 2].

  * The 1-compression of a is [1, 5, 3, 4, 2] and it is a permutation. 
  * The 2-compression of a is [1, 3, 3, 2] and it is not a permutation, since 3 appears twice. 
  * The 3-compression of a is [1, 3, 2] and it is a permutation. 
  * The 4-compression of a is [1, 2] and it is a permutation. 
  * The 5-compression of a is [1] and it is a permutation. 
#include "bits/stdc++.h"

#define ll long long
#define pb push_back
using namespace std;
const int mxN = 300001;
int arr[mxN]; // input array
int cnt[mxN]; // cnt[x] = number of occurrences of x in the array
bool ans[mxN]; // the final answer
int n;

void solve() {
    int n;
    cin >> n;
    for (int i = 0; i <= n; ++i) {
        cnt[i] = 0;
        ans[i] = 0;
    }
    for (int i = 0; i < n; ++i) {
        cin >> arr[i];
        arr[i]--;
        cnt[arr[i]]++;
    }
    int tp = -1;
    while (cnt[tp + 1] == 1)
        tp++;
    ans[0] = tp == n - 1;
    int l = 0;
    int r = n - 1;
    ans[n - 1] = cnt[0] > 0;
    for (int i = n - 1; i > 0; --i) {
        if (!ans[n - 1]) break;
        ans[i] = true;
        int nxt = n - i - 1;
        if (--cnt[nxt] == 0 && (arr[l] == nxt || arr[r] == nxt) && cnt[nxt + 1]) {
            if (arr[l] == nxt)l++;
            if (arr[r] == nxt)r--;
            continue;
        }
        break;
    }
    for (int i = 0; i < n; ++i)
        cout << ans[i];
    cout << endl;
}


signed main() {
    ios_base::sync_with_stdio(false);
    int t;
    cin >> t;
    while (t--)
        solve();
}