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: Time Limit Exceeded)

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

val = 0
rui = 1
mod = 0

nagasa = 2*10**5+1
#nagasa = 5
d_li = [0]*(nagasa)

for i in range(1,nagasa):
    t_v = i
    t_m = bin(t_v).count("1")
    ans = 0
    while t_v != 0:
        if d_li[t_v] != 0:
            ans += d_li[t_v]
            break
        ans += 1
        t_v %= t_m
        t_m = bin(t_v).count("1")
    d_li[i] = ans

#print(d_li)
#exit()

for i in range(n):
    val += int(x[n-1-i])*rui
    rui *= 2
    if int(x[n-1-i]) == 1:
        mod += 1

rui = 1
ans_li = []
    
for i in range(n):
    t_v = val
    t_m = mod
    if int(x[n-1-i]) == 1:
        t_v -= rui
        t_m -= 1
    else:
        t_v += rui
        t_m += 1
    rui *= 2
    ans = 0
    #while t_v != 0:
    if t_v != 0:
        t_v %= t_m
        ans += 1
    
    ans += d_li[t_v]
    #t_m = bin(t_v).count("1")
    ans_li.append(ans)
    #print(ans_li)

#print(ans_li)
for i in range(n):
    print(ans_li[n-1-i])