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)

n = int(input())
x = int(input(),2)
# b = int(2**(n-1))
pc = 0
d = []
c = x
for i in range(n):
    d.append(c&1)
    if c&1 == 1:
        pc += 1
    c=c>>1

mp =  x%(pc+1)
mm = x%(pc-1)
# print(x,pc,mp,mm)
for i in range(n):
    if d[-i-1]==0:
        m = 1
        temp = (mp+pow(2,n-i-1,pc+1)) % (pc+1)
    else:
        m = -1
        temp = (mm-pow(2,n-i-1,pc+1)) % (pc-1)
    # temppc = pc+m
    # temp = x^b
    ans = 1
    # print(temp,x,b)
    # print(temp,mp,pc,pow(2,n-i,pc+1))
    while temp:
        
        c = temp
        temppc = 0
        while c:
            if c&1 == 1:
                temppc += 1
            c=c>>1
        # print(temp)
        # print(i,temp,ans,temppc)
        # print(temp)
        # s = str(bin(temp))
        # print(temp,popcount(temp))
        if temppc == 0:
            break
        temp = temp % temppc
        ans += 1
        # c = temp
        # temppc = 0
        # while c:
        #     if c&1 == 1:
        #         temppc += 1
        #     c=c>>1
        # print(temp,s)
        # break
    # b=b>>1
    print(ans)