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: Runtime Error)

n = int(input())
x = input()

def popcount(i):
    return bin(i)[2:].count("1")

poplist = [0]*(n+1)
for i in range(1,n+1):
    k = i%popcount(i)
    poplist[i] = poplist[k]+1

import sys
if n ==1:
    if x=="0":
        print(0)
    else:
        print(1)
    sys.exit()

p = x.count("1")
nbit = int(x,2)
namari1 = nbit%(p-1)
namari2 = nbit%(p+1)

for i in range(n):
    a = str(x[:i]) + str(int(not int(x[i]))) + str(x[i+1:])
    a = int(a,2)
    P = n-1-i
    if int(x[i]) == 1:
        if p == 1:
            print(1)
            continue
        else:
            #p>=2
            c = (namari1 - 2**P%(p-1))%(p-1)
    else:
        #int(x[i])==0
        c = (namari2 + 2**P%(p+1))%(p+1)
    print(poplist[c]+1)