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 <bits/stdc++.h>
const int INF = 1e9;
const int MODk = 1e9+7;
using LL = long long;
const LL LINF = 1e18;
const double EPS = 1e-10;
using namespace std;
#define COUT(v) cout<<(v)<<endl
#define COUTDOUBLE(v) cout << std::setprecision(10)<<(v)<<endl;
#define CIN(n)  int(n);cin >> (n)
#define LCIN(n) LL(n);cin >> (n)
#define SCIN(n) string(n);cin >> (n)
#define YES(n) cout<<((n)? "YES" : "NO")<<endl
#define Yes(n) cout<<((n)? "Yes" : "No")<<endl
#define POSSIBLE(n) cout << ((n) ? "POSSIBLE" : "IMPOSSIBLE"  ) << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible"  ) <<endl

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) for(int i=0;i<(n);++i)
#define REPR(i,n) for(int i=n;i>=0;i--)

#define FOREACH(x,a) for(auto& (x) : (a) )

#define ALL(obj) (obj).begin(),(obj).end()

#define P pair<LL,LL>
#define I vector<int>
#define pb(v) push_back(v)
#define V vector
#define rt return
#define rmsame(a) sort(ALL(a)),a.erase(unique(ALL(a)), a.end())
#define ENDL cout<<endl

typedef string::const_iterator State;
class PalseError {};
class Edge{
public:
    int from,to,value;
    Edge(LL a,LL b,LL c){
        from = a;
        to = b;
        value = c;
    }
    Edge(LL a,LL b){
        from = a;
        to = b;
    }
};
int main(){
    CIN(N);
    I vec;
    REP(a,N){
        CIN(b);
        vec.push_back(b);
    }
    int ans = 0;
    int hoge = -1;
    if(vec.at(0) < vec.at(1)){
        hoge = 1;
    }
    if(vec.at(0) > vec.at(1)){
        hoge = 2;
    }
    if(vec.at(0) == vec.at(1)){
        hoge = -1;
    }
    REP(a,N-1){
        if(hoge == 1 && vec.at(a) > vec.at(a+1)){
            ans++;
            hoge = -1;
        }
        if(hoge == 2 && vec.at(a) < vec.at(a+1)){
            ans++;
            hoge = -1;
        }
        if(vec.at(a) < vec.at(a+1)){
            hoge = 1;
        }
        if(vec.at(a) > vec.at(a+1)){
            hoge = 2;
        }
    }
    COUT(ans+1);
    rt 0;
}