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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int lmod(string s, int x){
  int i,a=0;
  for(i=0;i<s.size()-1;i++){
    if (s[i] == '1')
      a++;
  	if (a>=x)
      a -= x;
  	a <<= 1;
  }
  if (s[i] == '1')
    a++;
  if (a>=x)
    a -= x;
  return a;
}

int popcount(int x){
  int res = 0;
  while(x>0){
    res += x & 1;
  	x >>= 1;
  }
  return res;
}

int main(){
  int N,i,j,ct,mct,s;
  string x,w;
  cin >> N >> x;
  
  for(i=0;i<N;i++){
    w = x;
    if (w[i] == '1')
      w[i]= '0';
    else
      w[i] = '1';
    ct = 0;
    mct = 0;
    for(j=0;j<N;j++)
      if (w[j] == '1')
        ct++;
    if ((ct == 0) || (ct == 1))
      cout << 1 << endl;
    else{
      //cout << w << " " << ct << endl;
      s = lmod(w,ct);
      mct = 1;
      while(s>0){
        s %= popcount(s);
        mct++;
      }
      cout << mct << endl;
    }
  }
  return 0;
}