Determine balanced k values in a permutation

You are given a permutation `p` of the integers `1..n`. For a number `k` (where `1 <= k <= n`), call `k` **balanced** if there exists a contiguous subarray `p[l..r]` such that: - `r - l + 1 = k`, and - the multiset of values in `p[l..r]` is exactly `{1, 2, ..., k}` (i.e., the subarray is a permutation of `1..k`). Your task: for every `k = 1..n`, determine whether `k` is balanced and return a binary string `s` of length `n` where: - `s[k-1] = '1'` if `k` is balanced - `s[k-1] = '0'` otherwise ### Input - An integer `n` - A permutation `p` of length `n` *(If your platform uses multiple test cases, solve independently per test case.)* ### Output - A binary string of length `n`. ### Example If `n = 5` and `p = [4, 1, 3, 2, 5]`, you should output a string of length 5 indicating which `k` are balanced. ### Constraints Assume `n` can be large (e.g., up to `2e5`), so an `O(n log n)` or `O(n)` approach is expected.