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.lang.Math

fun main(args: Array<String>) {
    val N = readInputLine().toInt()
    val a = readInputLine().toCharArray()

    val conCat = IntArray(N - 1)

    for (i in 0 until N - 1) {
        conCat[i] = Math.abs(a[i] - a[i + 1])
    }

    if (N == 2) {
        println(conCat[0])
        return
    }

    var ans = 0

    for (i in 0 until N - 2) {
        ans = Math.abs(ans - Math.abs(conCat[i] - conCat[i + 1]))
    }

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}