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: Wrong Answer)

import java.util.Scanner

fun main(args: Array<String>) {
    val scanner = Scanner(System.`in`)
    val n = scanner.nextInt()
    val str = scanner.next()
    val start = (0 until n).map { Integer.parseInt(str[it].toString()) }
    val lastNum = start.toMutableList()
    while (true) {
        if (lastNum.size == 0) {
            println(0)
            break
        }
        if (lastNum.size == 1) {
            print(lastNum[0])
            break
        }

        val a = mutableListOf<Int>()
        for (i in 0..(lastNum.size - 2)) {
            if (lastNum[i] != lastNum[i + 1]) {
                a.add(lastNum[i])
            }
        }
        a.add(lastNum[lastNum.size - 1])
        val b = (0..(a.size - 2)).map {
            Math.abs(a[it] - a[it + 1])
        }
        lastNum.clear()
        lastNum.addAll(b)
    }
}