Problem:
Score : 400 points

Problem Statement

Let \mathrm{popcount}(n) be the number of 1s in the binary representation of n.
For example, \mathrm{popcount}(3) = 2, \mathrm{popcount}(7) = 3, and \mathrm{popcount}(0) = 0.

Let f(n) be the number of times the following operation will be done when we repeat it until n becomes 0: "replace n with the remainder when n is divided by \mathrm{popcount}(n)." (It can be proved that, under the constraints of this problem, n always becomes 0 after a finite number of operations.)

For example, when n=7, it becomes 0 after two operations, as follows:

\mathrm{popcount}(7)=3, so we divide 7 by 3 and replace it with the remainder, 1.

\mathrm{popcount}(1)=1, so we divide 1 by 1 and replace it with the remainder, 0.

You are given an integer X with N digits in binary.
For each integer i such that 1 \leq i \leq N, let X_i be what X becomes when the i-th bit from the top is inverted.
Find f(X_1), f(X_2), \ldots, f(X_N).

Constraints

1 \leq N \leq 2 \times 10^5

X is an integer with N digits in binary, possibly with leading zeros.

Input

Input is given from Standard Input in the following format:

N
X

Output

Print N lines. The i-th line should contain the value f(X_i).

Sample Input 1

3
011

Sample Output 1

2
1
1

X_1 = 7, which will change as follows: 7 \rightarrow 1 \rightarrow 0. Thus, f(7) = 2.

X_2 = 1, which will change as follows: 1 \rightarrow 0. Thus, f(1) = 1.

X_3 = 2, which will change as follows: 2 \rightarrow 0. Thus, f(2) = 1.

Sample Input 2

23
00110111001011011001110

Sample Output 2

2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
3

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

const input = require("fs").readFileSync("/dev/stdin", "utf8")

;(input => {

    const lines = input.split('\n')
    const N = lines[0] - 0
    const X = lines[1].trim()

    const popcount = n => {
        let count = 0
        do {
            n & 1 ? count++ : count
        } while  (n = n >>> 1)
        return count
    }

    const f = n => {
        if (n === 0) {
            return 0
        }
        let count = 1
        while (n %= popcount(n)) count++
        return count
    }

    const x = parseInt(X, 2)
    const pr = popcount(x) - 1
    const nx = popcount(x) + 1
    for (let i = 0; i < N; i++) {
        let n = x ^ Math.pow(2, N - i - 1)
        if (n === 0) {
            console.log(0)
        } else {
            console.log(f(n % (X[i] === '1' ? pr : nx)) + 1)
        }
    }

})(input)