Balanced Prefix Sets in a Permutation

For each k, given a permutation of 1..n, determine whether some contiguous subarray has a value set of exactly {1..k}, and output the results in order as an n-character 01 string.

This site's standard input/output is stated explicitly.

输入格式

The first line contains n, and the second line contains a permutation of 1..n. This site's range is 1≤n≤100000.

输出格式

Output a 01 string of length n, where the k-th character indicates whether some contiguous subarray has value set {1..k}.

样例 1

输入：

4
2 1 4 3

输出：

1101

样例 2

输入：

5
3 1 2 5 4

输出：

11101

样例 3

输入：

1
1

输出：

1

样例说明

Example 1: the positions are contiguous for k equal to 1, 2, and 4, so the output is 1101. Example 2: they are contiguous for k equal to 1, 2, 3, and 5, so the output is 11101. Example 3: the only element forms the set {1} by itself, so the output is 1.