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 C# (Mono-mcs 6.8.0.105) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
class d{
    public static void Main(){
        int n = int.Parse(Console.ReadLine());
        char[] str = Console.ReadLine().Select(c => c).ToArray();
        int[] dp = new int[n+1];
        for(int i=1; i<=n; i++){
            int target = i;
            int cost = 0;
            while(target != 0){
                string bits = Convert.ToString(target,2);
                int count = bits.Count(c => c == '1');
                target %= count;
                cost++;
            }
            dp[i] = cost;
        }
        int ans;
        for(int i=0; i<n; i++){
            ans = 1;
            str[i] = str[i] == '1' ? '0' : '1';
            int ones = str.Count(ch => ch=='1');
            int tgt = Convert.ToInt32(new String(str), 2);
            tgt %= ones;
            if(tgt != 0){
                ans += dp[tgt];
            }
            str[i] = str[i] == '1' ? '0' : '1';
            Console.WriteLine(ans);
        }
    }
}