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>

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define RREP(i, n) for (int i = (n); i >= 0; --i)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (a); i >= (b); --i)
#define ALL(v) (v).begin(), (v).end()
#define RALL(a) (a).rbegin(), (a).rend()

#define uint8_t unsigned char
#define uint16_t unsigned short
#define uint32_t unsigned int
#define uint64_t unsigned long long

#define int8_t signed char
#define int16_t signed short
#define int32_t signed int
#define int64_t signed long long



using namespace std;
// #define PI 3.14159265358979323846
// cout << fixed << setprecision(20);


void f(int n, int& count)
{
    if (n == 0) {
        return;
    }
    bitset<20010> bs(n);
    int bit_count = bs.count();
    // cout << bit_count << endl;
    ++count;
    int next_n = n % bit_count;
        // cout << next_n << endl;
    f(next_n, count);
}




int main(int argc, char const* argv[])
{
    int n = 0;
    string x = "";
    cin >> n;
    cin >> x;

    for (int i = 0; i < n; ++i)
    {
        int count = 0;
        bitset<20010> bs(x);
        bs.flip(n-i-1);
        // cout << bs.to_ulong() << endl;
        f(bs.to_ulong(), count);
        cout << count << endl;
    }
    return 0;
}