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: Time Limit Exceeded)

package main

import (
  "fmt"
  "sync"
)

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

func goCalc(wg *sync.WaitGroup, i, j int, botVal int, X []int) {
  for ; i < j-1; i++ {
    X[i] = abs(X[i] - X[i+1])
  }
  X[j-1] = abs(X[j-1] - botVal)
  wg.Done()
}

func main() {
  var N int
  
  m := make([][]int, 4)
  for i := 0; i < 4; i++ {
    m[i] = make([]int, 4)
    for j := 0; j < 4; j++ {
      m[i][j] = abs(i - j)
    }
  }
  
  fmt.Scanf("%d\n", &N)
  
  X := make([]int, N)
  var input string = ""
  fmt.Scanf("%s\n", &input)
  for i := 0; i < N; i++ {
    X[i] = int(input[i] - '0')
  }
  
  wg := new(sync.WaitGroup)
  div := N / 10000
  if div == 0 {
    div = 1
  }
  step := int(N/div)
  for i := 1; i < N; i++ {
    wg.Add(div)
    idx := 0
    for j := 0; j < div-1; j++ {
    	go goCalc(wg, idx, idx + step, X[idx + step -1], X)
      idx += step
    }
    go goCalc(wg, idx, N-i+1, X[N-i], X)
    wg.Wait()
  }
  
  fmt.Println(X[0])
}