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.Integer
import java.lang.Long

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

    // i>=2 の場合、a_i,jは[0,2]となり、この計算は差を見るため全体を1引いても問題なし
    val a = readInputLine().map { it - '1' }.toIntArray()

    val isOdd = a.foldIndexed(false) {
        index, acc, a ->
        if (a % 2 == 0) {
            acc
        } else {
            if (lucas(N - 1, index, 2) == 1) {
                !acc
            } else {
                acc
            }
        }
    }

    if (isOdd) {
        println(1)
    } else {
        if (a.contains(1)) {
            println(0)
        } else {
            println(2)
        }
    }
}

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

// nCm mod p (p is prime number)
fun lucas(n: Int, m: Int, p: Int): Int {
    if (m > n) {
        return 0
    }

    var ret = 1L

    val nDec = Integer.toString(n, p)
    val mDec = Integer.toString(m, p).padStart(nDec.length, '0')

    for (i in 0 until nDec.length) {
        val nNum = Long.parseLong(nDec[i].toString(), p)
        val mNum = Long.parseLong(mDec[i].toString(), p)

        if (mNum > nNum) {
            return 0
        }

        for (j in LongRange(1L, nNum)) {
            ret *= j
        }
        for (j in LongRange(1L, mNum)) {
            ret /= j
        }
        for (j in LongRange(1L, mNum - nNum)) {
            ret /= j
        }
    }

    return ret.toInt()
}