Balanced Numbers (Permutation-of-[1..k] Subarrays)

You are given a permutation p in which each integer 1..n appears exactly once. For each length k=1..n, if some contiguous subarray has an element set exactly equal to {1,2,…,k}, the k-th character of the answer string is 1; otherwise it is 0.

The catalog's original examples and outputs are kept; this site explicitly defines the permutation domain as 1..n and adds n≤2000 to match the O(n²) algorithm and the I/O. The claim "any single element is balanced" in the original example explanation is imprecise: by the set definition, only the value 1 is balanced for length 1, but a permutation always contains 1, so the existence output is still 1.

输入格式

The first line is n, and the second line is a permutation p of 1..n. Bounds on this site: 1≤n≤2000.

输出格式

Output a 0/1 string of length n; the k-th character from the left corresponds to length k.

样例 1

输入：

4
4 1 3 2

输出：

1011

样例 2

输入：

3
2 3 1

输出：

101

样例 3

输入：

2
2 1

输出：

11