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: Runtime Error)

private fun readLn() = readLine()!!
private fun readInt() = readLn().toInt()
private fun readLong() = readLn().toLong()
private fun readStrings() = readLn().split(" ")
private fun readInts() = readStrings().map(String::toInt)
private fun readLongs() = readStrings().map(String::toLong)

fun main() {
    val n = readInt()
    val s = readLn()
    val popcnt = s.sumBy { if (it == '1') 1 else 0 }
    val mds = ArrayList<Int>()
    val p2s = ArrayList<IntArray>()
    for (m in popcnt-1..popcnt+1) {
        if (m <= 0) {
            mds.add(-1)
            break
        }
        var cur = 0
        for (c in s) {
            cur *= 2
            if (c == '1')
                cur++
            cur %= m
        }
        mds.add(cur)
        val p2 = IntArray(n)
        p2[0] = 1
        for (i in 1 until n) {
            p2[i] = p2[i - 1] * 2 % m
        }
        p2s.add(p2)
    }
    fun popCount(x : Int) : Int = if (x > 0) x % 2 + popCount(x / 2) else 0
    fun brute(x: Int) : Int = if (x == 0) 0 else 1 + brute(x % popCount(x))
    for (i in 0 until n) {
        val cmd = if (s[i] == '1') popcnt - 1 else popcnt + 1
        if (cmd == 0) {
            println(0)
            continue
        }
        var cans = if (s[i] == '1') mds[0] else mds[2]
        if (s[i] == '1') {
            cans -= p2s[0][n - i - 1]
        } else {
            cans += p2s[2][n - i - 1]
        }
        cans += cmd
        cans %= cmd
        println(brute(cans) + 1)
    }
}