Problem:
Score : 300 points

Problem Statement

Given is a permutation P_1, \ldots, P_N of 1, \ldots, N.
Find the number of integers i (1 \leq i \leq N) that satisfy the following condition:

For any integer j (1 \leq j \leq i), P_i \leq P_j.

Constraints

1 \leq N \leq 2 \times 10^5

P_1, \ldots, P_N is a permutation of 1, \ldots, N.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1 ... P_N

Output

Print the number of integers i that satisfy the condition.

Sample Input 1

5
4 2 5 1 3

Sample Output 1

3

i=1, 2, and 4 satisfy the condition, but i=3 does not - for example, P_i > P_j holds for j = 1.

Similarly, i=5 does not satisfy the condition, either. Thus, there are three integers that satisfy the condition.

Sample Input 2

4
4 3 2 1

Sample Output 2

4

All integers i (1 \leq i \leq N) satisfy the condition.

Sample Input 3

6
1 2 3 4 5 6

Sample Output 3

1

Only i=1 satisfies the condition.

Sample Input 4

8
5 7 4 2 6 8 1 3

Sample Output 4

4

Sample Input 5

1
1

Sample Output 5

1

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

#include <bits/stdc++.h>
#define ss second
#define ff first
#define all(x) x.begin(), x.end()
 
using namespace std;
using ll = long long;
using pii = pair<int, int>;
 
const int oo = 1e9 + 7;
const int mod = 1e9 + 7, maxn = 100100;
const long double PI = acos(-1);

int lis(vector<int> v, vector<int>& memo, int pos, int last){
    if (pos == (int)v.size() - 1 and v[pos] <= last) return 1;
    if (pos == (int)v.size() - 1) return 0;
    if (memo[pos] != -1) return memo[pos];
    if (v[pos] > last) return lis(v, memo, pos+1, last);
    return max(lis(v, memo, pos+1, last), lis(v, memo, pos+1, v[pos]) + 1);
}
 
int main (){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int n;

    cin >> n;

    vector<int> v(n), memo(n+1, -1);

    for (auto& x: v) cin >> x;


    cout << lis(v, memo, 0, oo) << endl;
    return 0;
}