Number of ways to distribute N items to three peoples under given conditions

I've been trying to solve a problem that states, determining the number of ways to distribute N items to three-person. The distribution would consider best if the total weight of items the first person gets is divisible by 3, the weight of items the second person got is divisible by 5 and the total weight of item the last person got is divisible by 7 & the amount of items each person gets should not be 0.

The first input N is considered the number of items & the 2nd line of input denotes N integers representing the weights of items. The i-th integer a[i] denotes the weight of i-th items. There were such constraints as,

3≤ N ≤12
1≤ a[i] ≤10^10

sample input 1:
6
2 3 5 7 9 13

sample output 1:
6

I tried a way to solve the problem but couldn't figure out how could the solution would be better so that the weight of the items that the first, second & third persons receive would be divisible by 3, 5 & 7 respectively. I tried so that one person gets the maximum amount of items among the three persons & each person gets at least one item, but couldn't figure out the "best" solution that the total weights of items each person gets would be divisible by 3, 5 & 7 respectively. Could you suggest what part of my code I should do the trick? Here's my solution to a simple distribution between three people. TIA

#include<bits/stdc++.h>

using namespace std;

int countWays(int N)
{
    int ans = ((N-1)*(N-2))/2;

    //storing the number of distribution that is not possible
    int s = 0;

    for(int i=2; i<=N-3; i++){
        for(int j=1; j<i; j++){
            //possibilities of 2 persons receiving the maximum
            if (N == 2 * i + j)
                s++;
        }
    }

    if(N%3 == 0)
        s = 3*s+1;
    else
        s = 3*s;

    //final ways to distribute
    return ans - s;
}

int main()
{
    int n, N=0;
    cin >> n;

    if(n<3 && n>12)
        return 0;

    vector<int> a(n);

    for(int i=0; i<n; i++){
        cin>>a[i];
        N += a[i];
    }

    cout<<countWays(N);

    return 0;
}