Help with "Jump on Buildings"

In short, can anyone please share their approach for this problem? I think my code gives the right answers but is slow (since it gives a TLE).

MY CODE
``````#include <bits/stdc++.h>
using namespace std;

#define FASTIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using ll = long long;

const int MAXN = 5e3+5;

int n;
vector<int> h(MAXN);
vector<int> jumps(MAXN);

int dp[MAXN][MAXN][2];

//dp[i][j][k]->dp[previous index][current index][direction]
int count(int i, int j, int k) {
if(abs(i-j) == 1) return dp[i][j][k] = 0;
if(dp[i][j][k] != -1) return dp[i][j][k];

dp[i][j][k] = 0;
if(k) {
for(int next=j-1; next>i; next--) {
if(h[next] < h[j])
dp[i][j][k] = max(dp[i][j][k], 1+count(j,next,!k));
}
}
else {
for(int next=j+1; next<i; next++) {
if(h[next] < h[j])
dp[i][j][k] = max(dp[i][j][k], 1+count(j,next,!k));
}
}
return dp[i][j][k];
}

int main() {
FASTIO

cin >> n;
for(int i=0; i<n; i++) cin >> h[i];

memset(dp,-1,sizeof(dp));

int maxJumps = 0;
for(int j=1; j<n; j++) {
if(h[j] < h[0])
maxJumps = max(maxJumps, 1+count(0,j,1));
}
jumps[0] = maxJumps;
maxJumps = 0;
for(int j=n-2; j>=0; j--) {
if(h[j] < h[n-1])
maxJumps = max(maxJumps, 1+count(n-1,j,0));
}
jumps[n-1] = maxJumps;

for(int i=1; i<n-1; i++) {
maxJumps = 0;
for(int j=0; j<i; j++) {
if(h[j] < h[i])
maxJumps = max(maxJumps, 1+count(i,j,0));
}
for(int j=i+1; j<n; j++) {
if(h[j] < h[i])
maxJumps = max(maxJumps, 1+count(i,j,1));
}
jumps[i] = maxJumps;
}

for(int i=0; i<n; i++) cout << jumps[i] << " ";
cout << "\n";

return 0;
}
``````