Infix to Postfix

#include <bits/stdc++.h>
using namespace std;

int precedence(char c)
{
    if(c=='^')
      return 3;
    else if(c=='*' || c=='/')
      return 2;
    else if(c=='+' || c=='-')
      return 1;
    else
     return -1;
}

string post_fix(string s)
{
    int n=s.length();
    stack<char>st;
    st.push('N');
    string ans;
    
    for(int i=0;i<n;i++)
    {
        if(isalpha(s[i]))
          ans+=s[i];
        else if(s[i]=='(')
           st.push('(');
        else if(s[i]==')')
        {
            while(st.top()!='N' && st.top()!='(')
            {
                char c=st.top();
                st.pop();
                ans+=c;
            }
            
            if(st.top()=='(')
            {
                st.pop();
            }
        }
        else
        {
            while(st.top()!='N' && precedence(s[i])<=precedence(st.top()))
            {
                char c=st.top();
                st.pop();
                ans+=c;
            }
            
            st.push(s[i]);
        }
           
    }
    
    while(st.top()!='N')
    {
        char c=st.top();
        st.pop();
         ans+=c;
    }
    
    return ans;
    
}





int main() {
	
int t; cin>>t;

 while(t--)
 {
     string s; cin>>s;
     cout<<post_fix(s)<<endl;
     
 }
	
	return 0;
}