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: Accepted)

fun main(args: Array<String>) {
	readLn()
	val a = readLn().map { it - '1' }
	if (a.min() == a.max()) return println(0)
	if (!a.contains(1)) return println(solve(a.map { it / 2 }) * 2)
	println(solve(a.map { it % 2 }))
}

private fun solve(a: List<Int>): Int {
	var two = 0
	var ans = 0
	val n = a.size - 1
	for (i in a.indices) {
		if (two == 0) ans = ans xor a[i]
		two += Integer.numberOfTrailingZeros(n - i) - Integer.numberOfTrailingZeros(i + 1)
	}
	return ans
}

private fun readLn() = readLine()!!
private fun readInt() = readLn().toInt()
private fun readStrings() = readLn().split(" ")
private fun readInts() = readStrings().map { it.toInt() }