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: Wrong Answer)

/***** author :  C0d1ngPhenomena *****/

    #include <bits/stdc++.h>
    #define endl "\n"
    #define ll long long int
    #define TestCases int T; cin>>T; while(T--)
    #define rep(i,n) for(ll i = 0; i < n; i++)
    #define revrep(i,n) for(ll i = n-1; i >= 0; i--)
    #define vll vector<ll>
    #define vvll vector < vll >
    #define pll pair<ll, ll>
    #define vpll vector <pll>
    #define mp(x,y) make_pair(x,y)
    #define mod 1000000007
    #define inf 1000000000000000001;
    #define all(c) c.begin(),c.end()
    #define alld(c) c.begin(),c.end(),greater<int>()
    #define mem(a,val) memset(a,val,sizeof(a))
    #define f first
    #define s second
    #define pb push_back
    using namespace std;
    
    ll countset(ll n)
    {
    	ll counta  = 0;

    	while(n)
    	{
    		if(n&1)
    			counta++;
    		n = n>> 1;
    	}

    	return counta;
    	
    }

    ll arr[100000];
    int main()
    {
        std::ios::sync_with_stdio(false);
        cin.tie(NULL);
        cout.tie(NULL);
        ll n;
        cin >> n;
        string arr;
       
       
        	cin >> arr;
        	
        

        
        rep(i,n)
        {
        	ll x = n ^ ( 1 << (n-1-i));
        	ll k = 0;

        	while(x)
        	{
        		ll y = countset(x);
        		// cout<<x<<" "<<y<<endl;
        		x %= y;
        		k++;
        	}

        	cout<<k<<endl;
        	
        }


        return 0;
    }