Problem:
Score : 700 points

Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3.
Let x_{i,j} defined as follows:

x_{1,j} := a_j \quad (1 \leq j \leq N)

x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

Constraints

2 \leq N \leq 10^6

a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N

Output

Print x_{N,1}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

fun main(args : Array<String>) {
    val n = readLine()!!.toInt()
    var aa = readLine()!!.map { it.toString().toInt() }.toMutableList()
    var queue = ArrayDeque<Int>()

    while (aa.size > 1) {
        var lastNum = -1

        aa.forEach {
            if (it == 0 && lastNum == 0) return@forEach
            queue.addLast(it)
            lastNum = it
        }

        if (queue.size == 0) {
            println(0)
            return
        }

        if (queue.size == 1) {
            println(queue.first())
            return
        }

        aa = mutableListOf()
        var num = queue.removeFirst()
        while (queue.isNotEmpty()) {
            aa.add(Math.abs(num-queue.first))
            num = queue.removeFirst()
        }
    }

    println(aa.first())
}