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)

fun main() {
    // 文字列
    var n = readLine()!!.toInt()
    val x = readLine()!!
    // 数値
//    val int =readLine()!!.toInt()
    // 行
//    val list = readLine()!!.split(" ").map (String::toInt )
//    val (a,b) = readLine()!!.split(" ").map(String::toInt)


    for (i in 0..n){
        //はんてん
        if (x[i]=='0'){
            x[i]=='1'
        }else{
            x[i]=='0'
        }
        val an=f(Integer.parseInt(x, 2))
        println(an)
    }
}

fun f(a:Int):Int{
    var count=0
    var n=a
    while (n!=0){
        n=popcount(n)
        count++
    }
    return count
}

fun popcount(n:Int):Int{
    var two= Integer.toBinaryString(n)
    val str=n.toString()
    var sum=0
    for (i in str){
        if (i=='1'){
            sum++
        }
    }
    return n%sum
}