convert from string to int

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C++

help me output is not coming in correct....

#include <iostream>
#include <string>
#include<conio.h>
using namespace std;
int main()
{

string first,second;
cout<<"Enter the first number"<<endl;;
cin>> first; // input=123
cout<<endl<<"Enter the Second Number"<<endl;
cin>> second; // input=324

int product= (int) first[2] * (int)second[2];
cout<<product; //output must be 12 because 3*4=12 please



getch();
return 0;
}