Balanced Prefix-Permutation Subarray for Every k

You are given a permutation p of length n (it contains each integer from 1 to n exactly once). A number k is called balanced if there exist indices l, r (1 ≤ l ≤ r ≤ n) such that the subarray p[l..r] contains exactly the set {1,2,...,k} (equivalently, p[l..r] is a permutation of 1..k). For each k from 1 to n, determine whether k is balanced. Return a binary string ans of length n where: ans[k] = '1' if k is balanced ans[k] = '0' otherwise Note: since p is a permutation, for k to be balanced there must be a subarray of length k whose elements are exactly 1..k. Input format (for implementation) Line 1: integer n Line 2: n integers representing p[1..n] Output format Output one binary string ans of length n. Examples Input: 5 1 2 3 4 5 Output: 11111 Input: 5 2 1 3 5 4 Output: 11101 Constraints p is a permutation of 1..n You must decide this for every k = 1..n. Example Input 5 1 2 3 4 5 Output 11111