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: Runtime Error)


// author-Shivam gupta

#include <bits/stdc++.h>


using namespace std;

#define MEM(a, b) memset(a, (b), sizeof(a))

#define FOREACH(it, l) for (auto it = l.begin(); it != l.end(); it++)

#define IN(A, B, C) assert( B <= A && A <= C)

#define MP make_pair
#define FOR(i,a) for(int i=0;i<a;i++)

#define FOR1(i,j,a) for(int i=j;i<a;i++)

#define EB emplace_back

#define INF (int)1e9

#define EPS 1e-9

#define PI 3.1415926535897932384626433832795

#define MOD 1000000007

#define read(type) readInt<type>()
#define max1 100001
#define out(x) cout<<x<<'\n'
#define out1(x) cout<<x<<" "
#define END cout<<'\n'
#define int long long
void fast(){
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}


signed main(){
int n ;
cin>>n;
string s;
cin>>s;
int cnt=0;
int ans=0;
int x=1,y=2;
for(int i=0;i<n;i++){
    if(s[i]=='1'){cnt++;}
}
for(int i=n-1;i>=0;i--){
    if(s[i]=='1'){ans+=x;}
    x*=y;
}
x=x/2;
int cur,c;
for(int i=0;i<n;i++){
    if(s[i]=='0'){cur=ans+x;c=cnt+1;}
    else{
        cur=ans-x;
        c=cnt-1;
    }
    x=x/2;
  //out1(cur);out1(c);
    int ans=0;
    while(cur!=0){
        cur=cur%c;
        int p=cur;
        c=0;
        ans++;
        while(p>0){
            if(p&1){c++;}
            p=p/2;

        }
   
    }
    out(ans);
}
}