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 s = scanner.next()
    val num = (0 until n).map {
        when (s[it]) {
            '1' -> 1
            '2' -> 2
            '3' -> 3
            else -> 0
        }
    }.toMutableList()

    while (true) {
        if (num.isEmpty()) {
            println(0)
            return
        } else if (num.size == 1) {
            print(num[0])
            return
        } else if (num.size == 2) {
            print(Math.abs(num[0] - num[1]))
            return
        }

        val a = mutableListOf(num[0])
        a.addAll(
            (1 until num.size)
                .asSequence()
                .filterNot { num[it - 1] == num[it] }
                .map { num[it] }
        )
        val b = (0..(a.size - 2))
            .map { Math.abs(a[it] - a[it + 1]) }
            .filterNot { it == 0 }

        if (b.toSet().size == 1) {
            println(0)
            return
        }

        num.clear()
        num.addAll(b)
    }
}