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 C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>

int popcount(int n) {
    std::stringstream ss;
    ss << std::bitset<32>(n);
    std::string s = ss.str();
    int ret = 0;
    for (size_t i = 0; i < s.size(); ++i) {
        if (s[i] == '1') {
            ++ret;
        }
    }

    return ret;
}

int count(const std::string& in, int pos) {
    std::string str = in;
    if (str[pos] == '0') {
        str[pos] = '1';
    } else {
        str[pos] = '0';
    }

    int num = std::stoi(str, nullptr, 2); 

    int cnt = 0;
    while (num != 0) {
        num %= popcount(num);
        ++cnt;
    }

    return cnt;
}

int main() {
    int N;
    std::string X;
    std::cin >> N >> X;

    for (int i = 0; i < N; ++i) {
        std::cout << count(X, i) << std::endl;
    }

    return 0;
}