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#include <iostream>
#include <cctype>
#include <string>
#include <list>
#include <stack>

using namespace std;

char pop(list<char> & a)                 //Pops the stack and returns it, I use it to append to output vector
{
char result = a.front();
a.pop_front();
return result;
}

int main()
{
int num;
string in;
cin >> num;

string out;                                              //stores outputed characters front operator stack
list<char> opr;
for(int zed=0; zed<num; zed++) {
cin >> in;

for(int i =0; i < in.length(); i++)
{
switch(in[i])                                         //Gets operator gets their precedence and pushes them into the stack(list) and
//output string
{
case '(': opr.push_front(in[i]);
break;
case ')':  while(opr.front()!='(' && !opr.empty())
{
out.push_back(pop(opr));
}

opr.pop_front();
break;
case '-': if(opr.front() == '+' || '*' || '^' || '/' || '%')
{
out.push_back(pop(opr));
opr.push_front(in[i]);
}
else opr.push_front(in[i]);
out.push_back(' ');
break;
case '+': if(opr.front() == '-' || '*' || '^' || '/' || '%')
{
out.push_back(pop(opr));
opr.push_front(in[i]);
}
else opr.push_front(in[i]);
out.push_back(' ');
break;
case '*': if(opr.front() == '^' || '/' || '%')
{
out.push_back(pop(opr));
opr.push_front(in[i]);
}
else opr.push_front(in[i]);
out.push_back(' ');
break;
case '^': opr.push_front(in[i]);
out.push_back(' ');
break;
case '/': if(opr.front() == '^' || '*' || '%')
{
out.push_back(pop(opr));
opr.push_front(in[i]);
}
else opr.push_front(in[i]);
out.push_back(' ');
break;
default: if(isdigit(in[i]) || isalpha(in[i]))   //Default: if character is a digit or a letter append it to output
out.push_back(in[i]);
}

}

while(!opr.empty())                     //if the stack isn't empty push the rest into the output vector
{
out.push_back(pop(opr));
opr.pop_front();
}

out.erase(remove(out.begin(), out.end(),'('), out.end());  //remove those stupid parenthesis
out.push_back('
');
}

cout << out;

return 0;
}

source