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 Go (1.6) (judge verdict: Runtime Error)

package main

import (
  "fmt"
)

func abs(a int) int {
  if a > 0 {
    return a
  }
  return -a
}

func recursive(i, j int, X [][]int) int {
  if i <= 1 {
    return X[0][j-1]
  }
  
  if X[i-2][j-1] < 0 {
    X[i-2][j-1] = recursive(i-1, j, X)
  }
  if X[i-2][j] < 0 {
    X[i-2][j] = recursive(i-1, j+1, X)
  }
  
  return abs(X[i-2][j-1] - X[i-2][j])
}

func main() {
  var N int
  
  fmt.Scanf("%d\n", &N)
  
  X := make([][]int, N)
  for i := 0; i < N; i++ {
    X[i] = make([]int, N)
    for j := 0; j < N; j++ {
      X[i][j] = -1
    }
  }
  for i := 0; i < N; i++ {
    var c byte
    fmt.Scanf("%c", &c)
    X[0][i] = int(c - '0')
  }
  
  fmt.Println(recursive(N, 1, X))
}