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#include <iostream>

#include <string>

using namespace std;

string number;

bool isValid(string num){

int sz = num.size();

bool should_double = true;

int check_sum = 0;

for(int i=sz-2; i>=0; i--){

int cur_digit = num[i]-'0'; //assume all are number digits

if(should_double==1){

cur_digit *= 2;

}

should_double = !should_double;

if(cur_digit>=10){

int tmp = cur_digit%10;

tmp += (cur_digit/10)%10;

cur_digit = tmp;

}

check_sum += cur_digit;

cout<<"adding digit "<<cur_digit<<endl;

}

check_sum += num[sz-1]-'0';

cout<<"debug: check sum = "<<check_sum<<endl;

if(check_sum % 10 == 0){

return true;

}else{

return false;

}

}

int main(){

if(isValid("")){

cout<<"Number "<<number<<" is valid!"<<endl;

}else{

cout<<"not valid"<<endl;

}

return 0;

}