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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline

#n = int(input())
#l = list(map(int, input().split()))

'''
a=[]
b=[]
for i in range():
    A, B = map(int, input().split())
    a.append(A)   
    b.append(B)'''
from copy import copy

n=int(input())
x=input().strip("\n")
cnt=0
for i in range(n):
    if x[i:i+1]=="1":
        cnt+=1

#xx=list(x)
pre=int(x,2)
#print(pre)
for i in range(n):
    if x[i:i+1]=="1":
        t=-1
        ad=-2**(n-1-i)
    else:
        t=1
        ad=2**(n-1-i)
    cnt+=t
    now=pre+ad
    ans=0
    use=copy(cnt)
    while now>0:
        #print(now,use)
        now%=use
        ans+=1
        use=0
        #print(bin(now)[2:])
        """for j in range(len(bin(now)[2:])):
            if bin(now)[2+j:3+j]=="1":
                use+=1"""
        bit=int(bin(now)[2:],2)
        #print(bit)
        while bit!=0:
            use+=1
            #print(bit)
            bit=bit&(bit-1)
    print(ans)
    cnt-=t