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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    private static class K {
        public int i;
        public int prev;

        public K(int i, int prev) {
            this.i = i;
            this.prev = prev;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            K k = (K) o;
            return i == k.i &&
                    prev == k.prev;
        }

        @Override
        public int hashCode() {
            return Objects.hash(i, prev);
        }
    }

    private static Map<K, Integer> memo = new HashMap<>();

    public static int lds(List<Integer> nums, int i, int n, int prev) {
        K key = new K(i, prev);
        if (memo.containsKey(key)) {
            return memo.get(key);
        }
        if (i == n) {
            return 0;
        }
        int excl = lds(nums, i + 1, n, prev);
        int incl = 0;
        if (nums.get(i) < prev) {
            incl = 1 + lds(nums, i + 1, n, nums.get(i));
        }

        memo.put(key, Integer.max(incl, excl));
        return memo.get(key);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        List<Integer> nums = new ArrayList<>(n);

        for (int i = 0; i < n; i++) {
            nums.add(sc.nextInt());
        }

        System.out.println(lds(nums, 0, nums.size(), Integer.MAX_VALUE));
    }

}