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: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vii;
typedef vector<ll> vll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define pb push_back
#define odd(x) ((x)&1)
#define even(x) (!odd(x))
#define all(v) (v).begin(),(v).end()
#define rep(i,n) for(auto i=0;i<n;++i)
#define FASTIO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define TEST_CASE int tc;cin>>tc;while(tc--)

template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

#ifdef LOCAL
#define cerr cout
#else
#endif

#define TRACE

#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif


void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}


template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
#define JD



ll calc(ll n)
{
    ll c=0;
    while(n)
    {
        ++c;
        ll r = __builtin_popcount(n);
        n%=r;
    }
    return c;
}


int main(int argv, char* argc[])
{
    FASTIO

    #ifndef JD
        freopen("in.txt","r",stdin);
        freopen("out.txt","w",stdout);
    #endif



    //Problem D
    ll n,cnt=0;
    string s;
    cin>>n>>s;
    rep(i,n) if(s[i]=='1') ++cnt;

    vll v(n);

    ll h = max(1ll,cnt-1);

    ll pd[n],pu[n];
    pd[0]=1,pu[0]=1;
    for(int i=1;i<n;++i)
    {
        pd[i]=(2*pd[i-1])%(h);
        pu[i]=(2*pu[i-1])%(cnt+1);
    }
    ll u=0,d=0,u0,d0;
    rep(i,n)
    {
        if(s[i]=='0') continue;
        u+=pu[n-1-i];u%=(cnt+1);
        d+=pd[n-i-1];d%=h;
    }
    u0=u,d0=d;

    rep(i,n)
    {
        if(s[i]=='0')
        {
            u+=pu[n-i-1];u%=(cnt+1);
            v[i]=calc(u)+1;
            u=u0;
        }
        else
        {
          if(cnt==1)
          {
            v[i]=0;
            continue;
          }  
          d=(d+h-pd[n-i-1])%h;
            v[i]=calc(d)+1;
            d=d0;
        }
    }
    for(auto i:v)
        cout<<i<<"\n";





    return 0;
}