Longest increasing subsequence

Hey I have tried to implement a dp solution. There's a little mistake which I can't figure out. Care to help me?

    #include <iostream>
#include<algorithm>
using namespace std;

int main() {
    // your code goes here
    int n;
    cin>>n;
int a[100];
for(int p=1;p<=n;p++)
cin>>a[p];
int dp[110];
for(int h = 1;h<=n;h++) dp[h] = 1;
for(int i = 1;i<=n;i++)
{

    for(int j =1;j<i;j++)
    {

        if(a[j]<a[i])
        {

            //dp[i] = max(dp[i],(dp[j]+1));
            if(dp[j]+1>dp[i])
            dp[i]=dp[j]+1;
        }
    }


    }
   int max= 0 ;
   for(int i=1;i<=n;i++)
   if(dp[i]>max)
   max=dp[i];
   cout<<max;
    return 0;
}