problem in regular expression to validate atomic

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C++

regular-expression

I want regular expression small_letter(small_letter,small_letter);
input:like(sara,bola);
output:atomic

input:like(sara,Bola);
output:other

#include<iostream>
#include<string>
#include<regex>
using namespace std;
int main()
{
    string s ;
    cout << "Enter a sentence to check: ";
    std::getline(cin, s);
    
    regex re("^(a-z)+\(+(a-z)+\,+(a-z)+\) $");
    bool m = regex_match(s,re);
    
    cout <<( m ? "atomic":"other") << endl;
    system("pause");
    return 0;
}