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: Accepted)

n = int(input())
x = input()
popcnt = x.count("1")

def powmod(lst,mod):
    if not mod: return
    d = 1
    for i in range(n)[::-1]:
        d %= mod
        lst[i] = d
        d *= 2

def xmod(mod):
    if not mod: return 
    res = 0
    d = 1
    for i in range(n)[::-1]:
        d %= mod
        if int(x[i]):
            res += d
            res %= mod
        d *= 2
    return res

def solve(x):
    res = 1
    while x != 0:
        popcnt = 0
        for i in range(20):
            if x>>i & 1: popcnt += 1
        x %= popcnt
        res += 1
    return res
    
powlst0 = [0]*n
powlst1 = [0]*n
powmod(powlst0,popcnt+1)
x0 = xmod(popcnt+1)
powmod(powlst1,popcnt-1)
x1 = xmod(popcnt-1)

for i in range(n):
    if int(x[i]):
        if popcnt == 1: print(0)
        else: print(solve((x1-powlst1[i])%(popcnt-1)))
    else: print(solve((x0+powlst0[i])%(popcnt+1)))