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 sc = Scanner(System.`in`)
    val n = sc.nextInt()
    val s = sc.next()
    var list = IntArray(n)
    var len = 0
    for(i in s.indices) {
        val d = s[i] - '0'
        list[i] = d
        ++len
    }
    while (len > 1) {
        val next = IntArray(len - 1){-1}
        var nextLen = 0
        for(i in 1 until len) {
            var d = list[i] - list[i-1]
            if(d < 0) d *= -1
//            if(d == 0) continue
            next[nextLen++] = d
        }
        list = next
        len = nextLen
    }
    if(len == 0) {
        list[0] = 0
    }
    print(list[0])
}