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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.lang.Error
import java.lang.Math.abs
import java.util.*


class LongMod(var num: Long, val MOD: Long = 1_000_000_007L) {
    init {
        if (MOD <= 0) throw Exception("MOD <= 0")
        this.num = (this.num%this.MOD + this.MOD)%this.MOD
    }
    constructor(numStr: String, Base: Int=10, MOD: Long=1_000_000_007L) :
            this(0L, MOD) {
        if (numStr.isEmpty()) return

        var rv = numStr.reversed()
        var d = 1L
        rv.forEach{ c ->
            this.num += (c - '0') * d
            this.num %= MOD
            d *= Base
            d %= MOD
        }
    }
    override operator fun equals(other: Any?): Boolean {
        if (other !is LongMod) return false
        return this.num % this.MOD == other.num % this.MOD
    }
    operator fun unaryMinus(): LongMod {
        return LongMod(-this.num)
    }
    private operator fun plusAssign(other: LongMod): Unit {
        if ((this.num + other.num) >= this.MOD) {
            this.num -= this.MOD
        }
        this.num += other.num
    }
    private operator fun minusAssign(other: LongMod): Unit {
        if ((this.num + this.MOD - other.num) >= this.MOD) {
            this.num -= this.MOD
        }
        this.num += this.MOD - other.num
    }
    private operator fun timesAssign(other: LongMod): Unit {
        this.num *= other.num
        this.num %= this.MOD
    }
    operator fun plus(other: LongMod): LongMod {
        val res = LongMod(this.num, this.MOD)
        res += other
        return res
    }
    operator fun minus(other: LongMod): LongMod {
        val res = LongMod(this.num, this.MOD)
        res -= other
        return res
    }
    operator fun times(other: LongMod): LongMod {
        val res = LongMod(this.num, this.MOD)
        res *= other
        return res
    }
    fun pow(n: Long): LongMod {
        if (n == 0L) return LongMod(1L, this.MOD)
        var x = this.pow(n / 2)
        x.timesAssign(x)
        if (n % 2 == 1L) x.timesAssign(this)
        return x
    }
    fun inv(): LongMod {
        return this.pow(this.MOD - 2)
    }
    operator fun divAssign(other: LongMod): Unit {
        this *= other.inv()
    }
    operator fun div(other: LongMod): LongMod {
        val res = LongMod(this.num, this.MOD)
        res /= other
        return res
    }
}

fun countOneBits(N: Long): Int {
    return (0 until 64)
            .filter { (N shr it) and 0b01L == 1L }
            .count()
}

fun main() {
    val N = rd.readInt()
    val X = rd.readString()
    assert(X.length == N)

    val Cnt1 = X.count{ it == '1'}.toLong()

    val base = mutableMapOf<Long, LongMod>()
    tAssert(Cnt1>1L){"Cnt1>1L"}

    if (Cnt1 > 1L) base[Cnt1-1] = LongMod(X, 2, Cnt1-1)
    if (Cnt1 > 0L) base[Cnt1] = LongMod(X, 2, Cnt1)
    base[Cnt1+1] = LongMod(X, 2, Cnt1+1)

    for (i in 0 until N) {
        val plus = X[i]=='1'
        val ncnt1 = if (plus) Cnt1 -1L else Cnt1 + 1L

        if (ncnt1 == 0L) {
            println(0)
            continue
        }

        val diff = LongMod(2L, ncnt1).pow(N-i-1L)
        val xm = if (plus) base[ncnt1]!! - diff
                          else base[ncnt1]!! + diff

        var ans = 1
        var xl = (xm.num + ncnt1) % ncnt1

        while (xl > 0L) {
            xl %= countOneBits(xl)
            ans++
        }

        println(ans)
    }
}


//val rd = debug.Reader("etc", "aising2020", "d", "sample-2")
val rd = Reader()


fun main(args: Array<String>) {
    try {
        val th = Thread(null, MainThread(), "mainThread", 128 * 1024 * 1024)
        th.setUncaughtExceptionHandler { _, e -> exception = e }
        th.start(); th.join()
        if (exception != null) throw exception!!
    } catch (e: Exception) { throw e }
}
var exception: Throwable? = null
const val MOD = 1_000_000_007L; const val INF = Int.MAX_VALUE/2; const val LINF = Long.MAX_VALUE/2
val EPS = 1e-9; fun DBLEQ(a: Double, b: Double): Boolean {return abs(a - b) < EPS}
data class IntPair(val first: Int, val second: Int)
data class To(val idx: Int, val cost: Long)
fun <T>edge(V: Int): Array<ArrayList<T>> { return Array(V){ArrayList<T>()} }
val errPrintln: (Any) -> Unit = { msg -> System.err.println(msg) }
fun rAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("EAssert Error: $msg"); throw Error(msg)}
}
fun tAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("TAssert Error: $msg"); Thread.sleep(3000)}
}
class MainThread : Runnable {
    override fun run() { main() }
}
class Reader {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    val readString: () -> String = { br.readLine() }
    val readInt: () -> Int = { br.readLine().toInt() }
    val readLong: () -> Long = { br.readLine().toLong() }
    val readIntArray: () -> IntArray = { br.readLine().split(' ').map { it.toInt() }.toIntArray() }
    val readLongArray: () -> LongArray = { br.readLine().split(' ').map { it.toLong() }.toLongArray() }
    val readListInt: () -> List<Int> = { br.readLine().split(' ').map { it.toInt() } }
    val readListLong: () -> List<Long> = { br.readLine().split(' ').map { it.toLong() } }
}