Problem:
Score : 200 points

Problem Statement

There are N mountains ranging from east to west, and an ocean to the west.

At the top of each mountain, there is an inn. You have decided to choose where to stay from these inns.

The height of the i-th mountain from the west is H_i.

You can certainly see the ocean from the inn at the top of the westmost mountain.

For the inn at the top of the i-th mountain from the west (i = 2, 3, ..., N), you can see the ocean if and only if H_1 \leq H_i, H_2 \leq H_i, ..., and H_{i-1} \leq H_i.

From how many of these N inns can you see the ocean?

Constraints

All values in input are integers.

1 \leq N \leq 20

1 \leq H_i \leq 100

Input

Input is given from Standard Input in the following format:

N
H_1 H_2 ... H_N

Output

Print the number of inns from which you can see the ocean.

Sample Input 1

4
6 5 6 8

Sample Output 1

3

You can see the ocean from the first, third and fourth inns from the west.

Sample Input 2

5
4 5 3 5 4

Sample Output 2

3

Sample Input 3

5
9 5 6 8 4

Sample Output 3

1

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdlib>
#include <time.h>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <array>
#include <string>
#include <iomanip>
#include <cstring>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define mp make_pair
#define eb emplace_back
#define F first
#define S second
using namespace std;
using namespace __gnu_pbds;

typedef long long int ll;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ost;

const ll maxN = 1e7;
const ll INF = 1e17;
const ll MOD = 1e9 + 7;

ll xs[] = {-1, 1, 0, 0, -1, 1, 1, -1};
ll ys[] = {0, 0, -1, 1, -1, 1, -1, 1};

ll segtree[maxN << 2];
ll lazy[maxN << 2];
ll A[maxN];

inline ll left(ll x){
	return x << 1;
}

inline ll right(ll x){
	return (x<<1) + 1;
}

void build(ll node, ll start, ll end){
	if(start == end)
		segtree[node] = A[start];
	else{
		ll mid = (start + end)/2;
		build(left(node), start, mid);
		build(right(node), mid+1, end);
		segtree[node] = segtree[left(node)] + segtree[right(node)];
	}
}

void update(ll node, ll start, ll end, ll l, ll r, ll val){
	if(lazy[node] != 0){
		segtree[node] += (end-start+1)*lazy[node];
		if(start != end){
			lazy[left(node)] += lazy[node];
			lazy[right(node)] += lazy[node];
		}
		lazy[node] = 0;
	}
	if(start > end or l > start or r < end)
		return ;
	else if(start >= l and r >= end){
		segtree[node] += val;
		if(start != end){
			lazy[left(node)] += val;
			lazy[right(node)] += val;
		}
	}
	else{
		ll mid=(start + end)/2;
		update(left(node), start, mid, l, r, val);
		update(right(node), mid+1, end, l, r, val);
		segtree[node] = segtree[left(node)] + segtree[right(node)];
	}
}

ll sums(ll node, ll start, ll end, ll l, ll r){
	if(lazy[node] != 0){
		segtree[node] += (end-start+1)*lazy[node];
		if(start != end){
			lazy[left(node)] += lazy[node];
			lazy[right(node)] += lazy[node];
		}
		lazy[node] = 0;
	}
	if(l > end or r < start or start > end)
		return 0;
	if(l <= start and r >= end)
		return segtree[node];
	ll mid = (start+end)/2;
	return sums(left(node), start, mid, l , r) + sums(right(node), mid + 1, end, l , r);
}

int main(){
	cin.sync_with_stdio(false);
	cin.tie(0);
	ll n;
	cin >> n;
	ll a[n];
	for(ll i=0; i<n; i++)
		cin >> a[i];
	ll maxx = 0;
	for(ll i=0; i<(1<<n); i++){
		ll cur = a[0], ans = 0;
		for(ll j=0; j<n; j++){
			if(i&(1<<j)){
				if(a[j] >= cur){
					ans++;
					cur = a[j];
				}
			}
		}
		maxx = max(maxx, ans);
	}
	cout << maxx;
	return 0;
}