Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.
          7
        3   8
      8   1   0
    2   7   4   4
  4   5   2   6   5
In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.

The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than 100.

A single line containing the largest sum using the traversal specified.

#include <iostream>

#include <string>

#include <cstdio>

#include <cmath>

#include <cstring>

#include <algorithm>

#include <vector>

#include <queue>

#define range(i,a,b) for(int i=a;i<=b;++i)

#define rerange(i,a,b) for(int i=a;i>=b;--i)

#define fill(arr,tmp) memset(arr,tmp,sizeof(arr))

using namespace std;

int n,dp[][];

void init(){

    cin>>n;

    range(i,,n)range(j,,i)cin>>dp[i][j];

    rerange(i,n-,)

    range(j,,i)dp[i][j]+=max(dp[i+][j],dp[i+][j+]);

}

void solve(){

    cout<<dp[][]<<endl;

}

int main() {

    init();

    solve();

    return ;

}