Collect maximum points in a grid using two traversals

Problem

   Given a matrix where every cell represents points. How to collect maximum points using two traversals under following conditions?
1) The first traversal starts from top left corner, i.e., (0, 0) and should reach left bottom corner, i.e., (R-1, 0). The second traversal starts from top right corner, i.e., (0, C-1) and should reach bottom right corner, i.e., (R-1, C-1)/

2) From a point (i, j), we can move to (i+1, j+1) or (i+1, j-1) or (i+1, j)

3) A traversal gets all points of a particular cell through which it passes. If one traversal has already collected points of a cell, then the other traversal gets no points if goes through that cell again.

Solution
     check bound at first is much easier.
Code

#include <stdio.h>
#include <iostream>
#include <cstring>
using namespace std;
const int R = 55;
const int C = 55;
int dp[R][C][C];
int a[R][C] = {{3, 6, 8, 2},
         {5, 2, 4, 3},
         {1, 1, 20, 10},
         {1, 1, 20, 10},
         {1, 1, 20, 10},
         };
int n,m;

int dfs(int row,int c1,int c2) {
    if (c1 < 0 || c1 >= m || c2 < 0 || c2 >= m) return -0x3f3f3f3f;
    if (row == n - 1 && c1 == 0 && c2 == m - 1) {
        return a[row][c1] + a[row][c2];
    }
    if (row == n - 1) return -0x3f3f3f3f;
    if (dp[row][c1][c2] != -1) return dp[row][c1][c2];
    int add = 0;
    if (c1 == c2) {
        add = a[row][c1];
    }
    else {
        add = a[row][c1] + a[row][c2]; 
    }
    
    int ans = -0x3f3f3f3f;
    ans = max(ans,add + dfs(row + 1,c1 - 1,c2 - 1));
    ans = max(ans,add + dfs(row + 1,c1 - 1,c2));
    ans = max(ans,add + dfs(row + 1,c1 - 1,c2 + 1));
    ans = max(ans,add + dfs(row + 1,c1,c2 - 1));
    ans = max(ans,add + dfs(row + 1,c1,c2));
    ans = max(ans,add + dfs(row + 1,c1,c2 + 1));
    ans = max(ans,add + dfs(row + 1,c1 + 1,c2 - 1));
    ans = max(ans,add + dfs(row + 1,c1 + 1,c2));
    ans = max(ans,add + dfs(row + 1,c1 + 1,c2 + 1));
    return dp[row][c1][c2] = ans;
}

int calc() {
    memset(dp,-1,sizeof(dp));
    return dfs(0,0,m - 1);
}

int main() {
    n = 5;
    m = 4;
    cout << calc() << endl;
 return 0;
}