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# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      //ABC031.D();
      Aising2020.D();
    }


    class Aising2020
    {
      public static void A()
      {
        var L = Read.Int();
        var R = Read.Int();
        var D = Read.Int();
        Console.WriteLine(R/D - (L-1)/D);
      }
      public static void B()
      {
        var N = Read.Int();
        var A = Read.IntN();
        Console.WriteLine(A.Select((x, i) => x % 2 == 1 && i % 2 == 0 ? 1 : 0).Sum());
      }
      public static void C()
      {
        var N = Read.Int();
        int[] count = new int[2000000];
        for(int x = 1; x <= 100; ++x)
        {
          for(int y = 1; y <= 100; ++y)
          {
            for(int z = 1; z <= 100; ++z)
            {
              var v = x * x + y * y + z * z + x * y + y * z + x * z;
              count[v]++;
            }
          }
        }
        Console.WriteLine(String.Join(Environment.NewLine, count.Skip(1).Take(N)));
      }
      public static void D()
      {
        var N = Read.Int();
        var X = Read.Str();
        var value = new int[N];
        var ans = Enumerable.Range(0, N).Select(i => -1).ToArray();
        int bit = 0;
        for(int i = 0; i < N; ++i) { bit += X[i] == '1' ? 1 : 0; }
        var p1 = bit + 1;
        var p2 = Math.Max(1, bit - 1);
        int a1 = 0, a2 = 0;
        for(int i = 0; i < N; ++i)
        {
          a1 = (a1 * 2 + (X[i] == '1' ? 1 : 0)) % p1;
          a2 = (a2 * 2 + (X[i] == '1' ? 1 : 0)) % p2;
        }
        var pow1 = 1;
        var pow2 = 1;
        for (int i = N - 1; i >= 0; --i)
        {
          if (X[i] == '1')
          {
            if (bit == 1) { ans[i] = 0; }
            else
            {
              var v = (a2 + p2 - (pow2 % p2)) % p2;
              int count = 1;
              while (v > 0)
              {
                var b = BitwiseOperation.Count1((ulong)v);
                v = v % b;
                count++;
              }
              ans[i] = count;
            }
          }
          else
          {
            var v = (a1 + pow1) % p1;
            int count = 1;
            while (v > 0)
            {
              var b = BitwiseOperation.Count1((ulong)v);
              v = v % b;
              count++;
            }
            ans[i] = count;
          }
          pow1 = (pow1 * 2) % p1;
          pow2 = (pow2 * 2) % p2;
        }
        Console.WriteLine(String.Join(Environment.NewLine, ans));
      }
      public static void E()
      {
        var T = Read.Int();
        for(int t = 0; t < T; ++t)
        {
          var N = Read.Int();
          var KLR = Enumerable.Range(0, N).Select(i => Read.LongN()).ToArray();
          
        }
      }
      public static void F()
      {

      }
    }








    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      //public static Dictionary<T, long> Frequency<T>(T[] array)
      //{
      //  var dict = new Dictionary<T, long>();
      //  foreach (var a in array)
      //  {
      //    if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
      //    dict[a]++;
      //  }
      //  return dict;
      //}
      public static MyDict<T, long> Frequency2<T>(T[] array)
      {
        var dict = new MyDict<T, long>();
        foreach (var a in array)
        {
          dict[a]++;
        }
        return dict;
      }

      public static long Power(long a, long n, long p)
      {
        long res = 1;
        long mult = a;
        for (int i = 0; i < 63; ++i)
        {
          if ((n & ((long)1 << i)) > 0)
          {
            res = (res * mult) % p;
          }
          mult = (mult * mult) % p;
        }
        return res;
      }
      public static long Inverse(long a, long p)
      {
        long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0)
        {
          e = a / b;
          f = b; b = a - e * b; a = f;
          f = d; d = c - e * d; c = f;
        }
        c %= p;
        return c + (c < 0 ? p : 0);
      }
      public static long[] Facts(int n, long p)
      {
        var facts = new long[n + 1];
        facts[0] = 1;
        for (int i = 1; i <= n; ++i)
        {
          facts[i] = (i * facts[i - 1]) % p;
        }
        return facts;
      }
      public static Func<int, int, long> Combin(int n, long P)
      {
        var fact = Facts(n, P);
        var inv = fact.Select(x => Inverse(x, P)).ToArray();
        return (N, M) =>
        {
          if (N < 0 || N < M || M < 0) { return 0; }
          return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
        };
      }

      public class MyDict<T1, T2> : Dictionary<T1, T2>
      {
        public new T2 this[T1 key]
        {
          get { if (!base.ContainsKey(key)) { base.Add(key, default(T2)); } return base[key]; }
          set { base[key] = value; }
        }
      }
      public class PriorityQueue<T> where T : IComparable
      {
        private IComparer<T> _comparer = null; private bool _isAsc = true; private T[] _heap; private int _sz = 0;
        public PriorityQueue(int maxSize, IComparer<T> comparer) { _heap = new T[maxSize]; _comparer = comparer; }
        public PriorityQueue(int maxSize, bool isAsc = true) { _heap = new T[maxSize]; _isAsc = isAsc; }
        private int Compare(T x, T y) { if (_comparer != null) { return _comparer.Compare(x, y); } return _isAsc ? x.CompareTo(y) : y.CompareTo(x); }
        public void Push(T x) { var i = _sz++; while (i > 0) { var p = (i - 1) / 2; if (Compare(_heap[p], x) <= 0) { break; } _heap[i] = _heap[p]; i = p; } _heap[i] = x; }
        public T Pop() { T ret = _heap[0]; T x = _heap[--_sz]; int i = 0; while (i * 2 + 1 < _sz) { int a = i * 2 + 1; int b = i * 2 + 2; if (b < _sz && Compare(_heap[b], _heap[a]) < 0) { a = b; } if (Compare(_heap[a], x) >= 0) { break; } _heap[i] = _heap[a]; i = a; } _heap[i] = x; return ret; }
        public int Count() { return _sz; }
        public T Peek() { return _heap[0]; }
        public bool Contains(T x) { for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true; return false; }
      }
      public class MyTuple<T1, T2> : IComparable where T1 : IComparable<T1>
      {
        public readonly T1 Item1; public readonly T2 Item2;
        public MyTuple(T1 item1, T2 item2) { Item1 = item1; Item2 = item2; }
        public int CompareTo(object obj) { return Item1.CompareTo(((MyTuple<T1, T2>)obj).Item1); }
      }
      public static long[] Dijkstra(Dictionary<int, Dictionary<int, long>> adj, int N, int M, int start)
      {
        long INF = 1000000000000000000;
        var dist = Enumerable.Range(0, N + 1).Select(i => INF).ToArray();
        var queue = new PriorityQueue<MyTuple<long, int>>(N + M + 100);
        dist[start] = 0;
        queue.Push(new MyTuple<long, int>(0, start));
        while (queue.Count() > 0)
        {
          var kvp = queue.Pop();
          var d = kvp.Item1; var v = kvp.Item2;
          if (dist[v] < d) { continue; }
          foreach (var kvp2 in adj[v])
          {
            var newV = kvp2.Key;
            var newD = dist[v] + kvp2.Value;
            if (newD < dist[newV])
            {
              dist[newV] = newD;
              queue.Push(new MyTuple<long, int>(newD, newV));
            }
          }
        }
        return dist;
      }
    }
    class Graph
    {
      public static HashSet<int> ConnectedComponent(Dictionary<int, HashSet<int>> adj, int idx)
      {
        HashSet<int> comp = new HashSet<int>();
        comp.Add(idx);
        List<int> target = new List<int>();
        target.Add(idx);
        while (target.Count > 0)
        {
          List<int> next = new List<int>();
          foreach (var p in target)
          {
            foreach (var f in adj[p])
            {
              if (!comp.Contains(f))
              {
                next.Add(f);
                comp.Add(f);
              }
            }
          }
          target = next;
        }
        return comp;
      }
      public static int[] CalcDistance_OnTree(Dictionary<int, HashSet<int>> adj, int N, int start)
      {
        var dist = Enumerable.Range(0, N + 1).Select(i => -1).ToArray();
        dist[start] = 0;
        Queue<int> queue = new Queue<int>();
        queue.Enqueue(start);
        while (queue.Count > 0)
        {
          var v = queue.Dequeue();
          foreach (var w in adj[v])
          {
            if (dist[w] < 0)
            {
              dist[w] = dist[v] + 1;
              queue.Enqueue(w);
            }
          }
        }
        return dist;
      }
      public static long[] CalcDistance_OnTree(Dictionary<int, Dictionary<int, long>> adj, int N, int start)
      {
        var dist = Enumerable.Range(0, N + 1).Select(i => -1L).ToArray();
        dist[start] = 0;
        Queue<int> queue = new Queue<int>();
        queue.Enqueue(start);
        while (queue.Count > 0)
        {
          var v = queue.Dequeue();
          foreach (var t in adj[v])
          {
            var w = t.Key;
            var c = t.Value;
            if (dist[w] < 0)
            {
              dist[w] = dist[v] + c;
              queue.Enqueue(w);
            }
          }
        }
        return dist;
      }
    }
    struct MOD
    {
      public static long P = 1000000007;
      public readonly long V;

      public MOD(long a) { this.V = a % P; }
      public static implicit operator MOD(long a) { return new MOD(a); }
      public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
      public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
      public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
      public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
      public MOD Inverse()
      {
        long a = V, p = P; long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0) { e = a / b; f = b; b = a - e * b; a = f; f = d; d = c - e * d; c = f; }
        c %= p;
        return c + (c < 0 ? p : 0);
      }
      public MOD Power(long n)
      {
        long a = V, p = P; long res = 1; long mult = a;
        for (int i = 0; i < 63; ++i) { if ((n & ((long)1 << i)) > 0) { res = (res * mult) % p; } mult = (mult * mult) % p; }
        return res;
      }
      public override string ToString() { return V.ToString(); }
    }
    class BitwiseOperation
    {
      public static int Count1(UInt64 x)
      {
        UInt64 y = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
        y = (y & 0x3333333333333333) + ((y >> 2) & 0x3333333333333333);
        y = (y & 0x0f0f0f0f0f0f0f0f) + ((y >> 4) & 0x0f0f0f0f0f0f0f0f);
        y = (y & 0x00ff00ff00ff00ff) + ((y >> 8) & 0x00ff00ff00ff00ff);
        y = (y & 0x0000ffff0000ffff) + ((y >> 16) & 0x0000ffff0000ffff);
        return (int)((y & 0x00000000ffffffff) + ((y >> 32) & 0x00000000ffffffff));
      }
      public static int MSB(UInt64 x)
      {
        if (x == 0) { return -1; }
        x |= (x >> 1);
        x |= (x >> 2);
        x |= (x >> 4);
        x |= (x >> 8);
        x |= (x >> 16);
        x |= (x >> 32);
        return Count1(x) - 1;
      }
    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M, bool isDirectional = false)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); if (!isDirectional) { dict[ab[1]].Add(ab[0], ab[2]); } }
return dict;
}
}
    }
}