Balanced Prefix Set in a Permutation

You are given a permutation p of length n (it contains each integer 1..n exactly once). For each k (1 <= k <= n), call k balanced if there exists a contiguous subarray p[l..r] such that the set of elements in that subarray is exactly {1,2,...,k} (in any order). For every k, determine whether it is balanced and return a binary string (or 0/1 array) ans of length n: ans[k] = '1' if k is balanced ans[k] = '0' otherwise Input format Line 1: integer n Line 2: n integers, the permutation p[1..n] Output format A binary string ans of length n for k=1..n. Constraints 1 <= n <= 2*10^5 p is a permutation of 1..n Sample tests (stdin/stdout) input 5 1 3 2 4 5 output 11111 input 5 2 1 4 3 5 output 10101 input 5 3 1 2 5 4 output 01101 input 1 1 output 1 input 6 4 1 3 2 6 5 output 011011 Example Input 5 1 3 2 4 5 Output 11111