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;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string X = Console.ReadLine();
		int ct = 0;
		int[]A = new int[N];
		for(var i=0;i<X.Length;i++){
			int s = int.Parse(X.Substring(i,1));
			if(s==1){
				A[i] = 1;
				ct++;
			}
		}
		int[,]B = new int[N,4];
		int t = 1;
		int a = 0;
		for(var j=N-1;j>=0;j--){
			if(A[j]==1){
				a = (a + t) % (ct+1);
            }
				B[j,0] = a;
				t = (t * 2) % (ct+1);
		}
		t = 1;
		a = 0;
		for(var j=N-1;j>=0;j--){
          	if(ct>1){
			if(A[j]==1){
				a = (a + t) % (ct-1);
            }
				B[j,1] = a;
			t = (t * 2) % (ct-1);
            } else {
              B[j,1] = 0;
            }
		}
		t = 1;
		for(var j=N-1;j>=0;j--){
			B[j,2] = t;
          	t = (t * 2) % (ct+1);
		}
		t = 1;
		for(var j=N-1;j>=0;j--){
          if(ct>1){
			B[j,3] = t;
          	t = (t * 2) % (ct-1);
          } else {
            B[j,3] = 0;
          }
		}
		int[]C = new int[100002];
		for(var i=1;i<=100001;i++){
			int at = i;
			int c = 1;
			int ca = 0;
			while(true){
				if(at/c%2==1){
					ca++;
				}
				c *= 2;
				if(c>at){
					break;
				}
			}
			int d = at % ca;
			C[at] = C[d]+1;
		}
		//for(var i=0;i<N;i++){
        //  Console.Error.WriteLine(B[i,0]+" "+B[i,1]+" "+B[i,2]+" "+B[i,3]);
        //}
		//for(var i=0;i<100;i++){
       //  Console.Error.WriteLine(C[i]);
       // }
		for(var i=0;i<N;i++){
			if(A[i]==0){
              	int a3 = B[0,0]+B[i,2];
              	//Console.WriteLine(a3);
				Console.WriteLine(C[a3%(ct+1)]+1);
			} else {
				if(ct==1){
                  	Console.WriteLine(1);
                } else {
              	int a3 = (B[0,1]-B[i,3]+(ct-1))%(ct-1);
              	//Console.WriteLine(a3);
				Console.WriteLine(C[a3%(ct-1)]+1);
                }
			}
		}
	}
}