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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

#

import sys
input=sys.stdin.readline

def main():
    N=int(input())
    X=input().strip("\n")[::-1]
    cnt=[0]*N
    for i in range(1,N):
        n=i
        while(n>0):
            pc=0
            for j in range(19):
                if (n>>j)&1==1:
                    pc+=1
            n%=pc
            cnt[i]+=1
    pc=X.count("1")
    t=0
    c=[0]*N
    for i in range(N):
        if X[i]=="1":
            t+=2**i
            c[i]=1
    X=t
    ans=[0]*N
    for i in range(N):
        if c[i]==1:
            x=X-pow(2,i)
            pci=pc-1
            x-=(x//pci)*pci
            ans[i]=cnt[x%pci]+1
        else:
            x=X+pow(2,i)
            pci=pc+1
            x-=(x//pci)*pci
            ans[i]=cnt[x%pci]+1
    ans=ans[::-1]
    for i in range(N):
        print(ans[i])
    
    
    
if __name__=="__main__":
    main()