Need help in a DP problem

Problem E of This Contest

problem statement


what I am doing wrong

#include <bits/stdc++.h>
using namespace std;
 
void solve(){ 
   int n;cin>>n; 
   vector<vector<int>> vec;
   vector<vector<int>> dp(n,vector<int>(n,-1000000));

for(int i=0;i<n;i++){
    vector<int> v;
     for(int j=0;j<=i;j++){
        int k;
        cin>>k;
        v.push_back(k);
    }
       vec.push_back(v);
}

 dp[0][0] = vec[0][0];
 int mx = -100000000;

 for(int i=1;i<n;i++){
    for(int j=0;j<=i;j++){
      if(j>0) dp[i][j] = max(dp[i-1][j-1]+vec[i][j],dp[i][j]);
      if(j<i) dp[i][j] = max(dp[i-1][j]+vec[i][j],dp[i][j]);
      if(i==n-1) mx = max(mx,dp[i][j]); 
    }
 }
 cout << mx;
}
 
 
int main(){
    ios_base::sync_with_stdio(0) ;
    cin.tie(0) ; cout.tie(0) ;
    cout.precision(20);
    int T=1;//cin>>T;
    while(T--){
        solve();
        if(T)cout << endl;
    }
    return 0;
}

Just add the case that if n==1 return vec[0][0] and not -100000000

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