Need help avoiding integer overflow for Project Euler 15

I've been running into troubles with Integer overflow. The code works up till an input of 16, but I need it to work up till 20.

#include <iostream>
#include <cmath>
#include <stdlib.h>
#include <stdio.h>

using namespace std;
int grid(int);

int main(){
    int size;
    cin >> size;
    grid(size);

return 0;
}

int grid(int array){
    array = array+1;
    unsigned long long int map[array][array];
    for(int i = 0; i < array; ++i){ 
    // initialize grid distance
        map[i][0] =1;
        map[0][i]= 1;}
    for(int i =1; i < array; ++i){
        for(int j =1; j < array; ++j){
            map[i][j] = map[i-1][j] +map[i][j-1];}
}
    array = array -1;
return map[array][array]; //Return value to main function
}