long getWays(int n, const vector<long> &c, const int i,
             vector<vector<long>> &lookupTable) {
    
    if (lookupTable[n - 1][i] != -1)
        return lookupTable[n - 1][i];
    
    long ways = 0;

    int faceValue = c[i];
    if (n % faceValue == 0)
        ++ways;

    for (long amount = 0; amount < n; amount += faceValue) {
        if (i > 0) {
            long waysToCombineRest = getWays(n - amount, c, i - 1, lookupTable);
            ways += waysToCombineRest;
        }                
    }
    lookupTable[n - 1][i] = ways;
    return ways;
}


long getWays(int n, vector<long> c) { 
    sort(c.begin(), c.end());
    vector<vector<long>> lookupTable(n, vector<long>(c.size(), -1));
    return getWays(n, c, c.size() - 1, lookupTable);
}