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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function Main(input) {
    input = input.split("\n");
    for (i=0; i < input.length; i=i+2) {
        var N = parseInt(input[i])
        var a = input[i+1].split("")
        var aa = a.map(Number)
        for (j=N; j > 1; j--) {
            for (k=0; k < j; k++) {
                var e = Math.abs(aa[0]-aa[1])
                aa.push(e)
                aa.shift()
            }
            aa.pop()
        }
        console.log(aa[0])
    }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));