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++ (Clang 10.0.0) (judge verdict: Runtime Error)

#include <iostream>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <deque>
#include <numeric>
#include <sstream>
#include <iomanip>
#define ALL(X) X.begin(), X.end()
using lint = long long;
template <typename T>
void print_container(std::vector<T> vec)
{
    for (auto iter = vec.begin(); iter != vec.end(); ++iter)
    {
        std::cout << *iter << " ";
    }
    std::cout << std::endl;
}

int main()
{
    lint n;
    scanf("%lld", &n);

    std::string s;
    std::cin >> s;

    lint len = s.size();
    lint s_pc = 0;

    for (int i = 0; i < n; ++i)
    {
        if (s[i] == '1')
        {
            s_pc++;
        }
    }

    lint p1 = s_pc + 1;
    lint m1 = s_pc - 1;

    std::vector<lint> p1_rem_vec(n, 0);
    std::vector<lint> m1_rem_vec(n, 0);

    lint p1_rem = 1 % p1;
    p1_rem_vec[n - 1] = p1_rem;
    for (int i = n - 2; i >= 0; --i)
    {
        p1_rem = (p1_rem * 2) % p1;
        p1_rem_vec[i] = p1_rem;
    }

    lint m1_rem = 1 % p1;
    m1_rem_vec[n - 1] = m1_rem;
    for (int i = n - 2; i >= 0; --i)
    {
        m1_rem = (m1_rem * 2) % m1;
        m1_rem_vec[i] = m1_rem;
    }

    std::vector<lint> pop_rem(n + 2, 0);
    for (int i = 1; i <= n + 1; ++i)
    {
        lint pop = 0;
        lint tmp = i;
        while (tmp > 0)
        {
            if (tmp % 2 == 1)
            {
                pop++;
            }
            tmp >>= 1;
        }
        lint out = i % pop;
        pop_rem[i] = pop_rem[out] + 1;
    }

    print_container<lint>(pop_rem);

    lint base_p1 = 0;
    lint base_m1 = 0;
    for (int i = 0; i < n; ++i)
    {
        if (s[i] == '1')
        {
            base_p1 += p1_rem_vec[i];
            base_m1 += m1_rem_vec[i];
        }
    }
    base_p1 %= p1;
    base_m1 %= m1;

    for (int i = 0; i < n; ++i)
    {
        if (s[i] == '0')
        {
            lint cur_p1_rem = base_p1 + p1_rem_vec[i];
            cur_p1_rem %= p1;
            std::cout << pop_rem[cur_p1_rem] + 1
                      << "\n";
        }
        else
        {
            lint cur_m1_rem = base_m1 - m1_rem_vec[i];
            if (cur_m1_rem < 0)
            {
                cur_m1_rem += m1;
            }
            std::cout << pop_rem[cur_m1_rem] + 1 << "\n";
        }
    }

    return 0;
}