Problem:
Score : 300 points

Problem Statement

You are given an array A of length N.
Your task is to divide it into several contiguous subarrays.
Here, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.
At least how many subarrays do you need to divide A into?

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Each A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible number of subarrays after division of A.

Sample Input 1

6
1 2 3 2 2 1

Sample Output 1

2

One optimal solution is to divide the array into [1,2,3] and [2,2,1].

Sample Input 2

9
1 2 1 2 1 2 1 2 1

Sample Output 2

5

Sample Input 3

7
1 2 3 2 1 999999999 1000000000

Sample Output 3

3

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
#include<cstdio>
#include<algorithm>
#define M 1000000007
#define N 3010
using namespace std;
int f[N][N][2],g[N][N][2][2];
int l,t,n,m,ans;
int main(){
    scanf("%d%d",&n,&m);
    f[0][0][1]=1;
    for (int i=1;i<=n;i++) f[0][i][0]=1;
    for (int i=0;i<=m-1;i++)
        for (int j=0;j<=n;j++)
            for (int k=0;k<=1;k++){
                if (j) (f[i+1][j-1][k|(j-1==0)]+=f[i][j][k])%=M;
                if (j) (f[i+1][j][k|(j==1)]+=f[i][j][k])%=M;
                if (n-j) (f[i+1][j][k]+=f[i][j][k])%=M;
                if (n-j) (f[i+1][j+1][k]+=f[i][j][k])%=M;
            }
    for (int i=0;i<=n;i++) (ans+=f[m][i][1])%=M;
    printf("%d",ans);
    return 0;
}