#include <iostream>
#include <string>
using namespace std;


bool isValid(const string& cardNumber)
{
    if ((sumOfDoubleEvenPlace(cardNumber) + SumOfOddPlace(cardNumber)) % 10 != 0)
    {
        return false;
    }
    else if ( startsWith(cardNumber) == false)
    {
        return false;
    }
    else if (cardNumber.length() > 16 || cardNumber.length() < 13)
    {
        return false;
    }
    else
    {
        return true;
    }


}
bool startsWith(const string& cardNumber, const string& substr)
{
    if (cardNumber[0] - '0' == 4 || cardNumber[0] - '0' == 5 || cardNumber[0] - '0' == 6 ||
        (cardNumber[0] - '0' == 3 && cardNumber[1] - '0' == 7))
    {
        return true;
    }
    else
    {
        return false;
    }
}

//----------------------------------------------------------------------------------------------------
int getDigit(int number)
{
    if ((number - '0') * 2 >= 10)
    {
        int A = (number - '0') * 2 - 10;
        int B = ((number - '0') * 2) / 10;
        int C = A + B;
        return C;
    }
    else
    {
        number = (number - '0') * 2;
        return number;
    }
}
//----------------------------------------------------------------------------------
int sumOfDoubleEvenPlace(const string& cardNumber)
{
    int Even = 0;
    int N = 0;
    while (N < cardNumber.length())
    {
        if (N == 0 || N % 2 == 0)
        {
            int number = cardNumber[N];
            Even = Even + getDigit(number);
        }

        N++;
    }
    return Even;
}
//----------------------------------------------------------------------------------
int SumOfOddPlace(const string& cardNumber)
{
    int Odd = 0;
    int N = 1;
    while (N < cardNumber.length())
    {
        if (N == 1 || N % 2 != 0)
        {
            Odd = Odd + cardNumber[N] - '0';
        }
        N++;
    }

    return Odd;
}
//-----------------------------------------------------------------------------------
int main()
{
    cout << " Enter a credit card # :";
    string cardNumber;
    getline(cin, cardNumber);

    if (isValid(cardNumber))
    {
        cout << cardNumber << " is a valid number \n";
    }

    else
    {
        cout << cardNumber << " is not a valid number \n";
    }

    return 0;

}