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. 
import java.util.*;
import java.io.*;
public class A {

















    static boolean tests = true;
    static class SegmentTree{
        private Pair[] tree;
        private int n, input[];
        public SegmentTree(int[] input){
            this.n = input.length;
            int[] temp = new int[n+1];
            for (int i = 1; i <= n; ++i){
                temp[i] = input[i-1];
            }
            this.input = temp;
            tree = new Pair[4*n+5];
            build(1, 1, n);
        }
        int l(int u){
            return 2*u;
        }
        int r(int u){
            return l(u)+1;
        }
        void build(int u, int left, int right){
            tree[u] = new Pair(left, right);
            if (left == right){
                tree[u].min = input[left];
                tree[u].max = input[left];
                tree[u].sum = input[left];
                return;
            }
            int mid = (left+right)/2;
            build(l(u), left, mid);
            build(r(u), mid+1, right);
            tree[u].min = Math.min(tree[l(u)].min, tree[r(u)].min);
            tree[u].max = Math.max(tree[l(u)].max, tree[r(u)].max);
            tree[u].sum = tree[l(u)].sum+tree[r(u)].sum;
        }
        void prop(int u){
            if (tree[u].left != tree[u].right){
                tree[l(u)].delta += tree[u].delta;
                tree[r(u)].delta += tree[u].delta;
                tree[u].min += tree[u].delta;
                tree[u].max += tree[u].delta;
                tree[u].delta = 0;
            }
        }
        void update(int u){
            if (tree[u].left != tree[u].right){
                tree[u].min = tree[l(u)].min+tree[l(u)].delta;
                tree[u].min = Math.min(tree[u].min,tree[r(u)].min+tree[r(u)].delta);
                tree[u].max = tree[l(u)].max+tree[l(u)].delta;
                tree[u].max = Math.max(tree[u].max,tree[r(u)].max+tree[r(u)].delta);
                tree[u].sum = tree[l(u)].sum+(tree[l(u)].right-tree[l(u)].left+1)*tree[l(u)].delta;
                tree[u].sum += tree[r(u)].sum+(tree[r(u)].right-tree[r(u)].left+1)*tree[r(u)].delta;
            }
        }
        int rangeMin(int u, int left, int right){
            if (tree[u].right < left || tree[u].left > right){
                return (int)1e9;
            }
            if (tree[u].left >= left && tree[u].right <= right){
                return tree[u].min+tree[u].delta;
            }
            prop(u);
            int min = rangeMin(l(u), left, right);
            min = Math.min(min, rangeMin(r(u), left, right));
            update(u);
            return min;
        }
        int rangeMax(int u, int left, int right){
            if (tree[u].right < left || tree[u].left > right){
                return (int)-1e9;
            }
            if (tree[u].left >= left && tree[u].right <= right){
                return tree[u].max+tree[u].delta;
            }
            prop(u);
            int max = rangeMax(l(u), left, right);
            max = Math.max(max, rangeMax(r(u), left, right));
            update(u);
            return max;
        }
        long rangeSum(int u, int left, int right){
            if (tree[u].right < left || tree[u].left > right){
                return 0L;
            }
            if (tree[u].left >= left && tree[u].right <= right){
                return tree[u].sum+(tree[u].right-tree[u].left+1)*tree[u].delta;
            }
            prop(u);
            long sum = rangeSum(l(u), left, right);
            sum += rangeSum(r(u), left, right);
            update(u);
            return sum;
        }
        void rangeAdd(int u, int left, int right, int add){
            if (tree[u].right < left || tree[u].left > right){
                return;
            }
            if (tree[u].left >= left && tree[u].right <= right){
                tree[u].delta += add;
                return;
            }
            prop(u);
            rangeAdd(l(u), left, right, add);
            rangeAdd(r(u), left, right, add);
            update(u);
        }
        private class Pair{
            int min, max, left, right;
            long sum;
            int delta = 0;
            public Pair(int l, int r){
                this.left = l;
                this.right = r;
                sum = 0L;
                min = (int)1e9;
                max = -min;
            }
        }
    }
    static PrintWriter out = new PrintWriter(System.out);
    static void solve(){
       int n = fs.nextInt();
       int[] a = fs.readIntArray(n);
       int left = 0, right = n-1;
       int[] b = new int[n];
       for (int i = 0; i < n; ++i){
           b[i] = a[i];
       }
       Arrays.sort(b);
       String ans = "1";
       for (int i = 0; i < n-1; ++i){
           if (b[i+1]-b[i] != 1){
               ans = "0";
               break;
           }
       }
       SegmentTree st = new SegmentTree(a);
       int ind = int_max;
       if (st.rangeMin(1, 1, n) == 1){
           for (int x = 1; x < n; ++x){
               int l = left, r = right;
               if (a[left] == x) ++left;
               else if (a[right] == x) --right;
               if (l == left && r == right){
                   ind = x;
                   break;
               }
               if (st.rangeMin(1, left+1, right+1) != x+1){
                   ind = x;
                   break;
               }
           }
       }else ind = 0;
       out.print(ans);
       int cnt = 1;
       for (int i = 2; i <= n-ind; ++i){
           ++cnt;
           out.print("0");
       }
      while (cnt < n){
          out.print("1");
          ++cnt;
      }
      out.println();
    }
























    static FastScanner fs = new FastScanner();
    static int int_max = (int)1e9+5;
    public static void main(String[] args) {
        int t = 1;
        if (tests) t = fs.nextInt();
        while (t-- > 0) solve();
        out.close();
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readIntArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long[] readLongArray(int n){
            long a[] = new long[n];
            for (int i = 0; i < n; ++i){
                a[i] = nextLong();
            }
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}