https://codeforc.es/gym/101987

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <map>
#include <set>
#include <stack>
using namespace std;

#define sfi(x) scanf("%d",&x)
#define sfc(x) scanf("%c",x)
#define sfl(x) scanf("%lld",&x)
#define sfs(x) scanf("%s",x)

#define pb push_back
#define fl() printf("flag!\n")
#define INF 0x3f3f3f3f
#define ll long long
#define mem(x,y) memset(x,y,sizeof(x))
#define FAST_IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)

const int maxn=2e5+9;
const int mod=1e9+7;

char s[maxn],tmp[maxn];
int n,cnt;


bool isc(char c)
{
    return c>='a'&&c<='z';
}

bool iso(char c)
{
    return c=='/'||c=='%'||c=='-'||c=='+'||c=='*';
}

bool ch1(char s[],int len)
{
    //for(int i=0;i<len;i++) cout<<s[i];

    if(s[0]==')') return 0;
    if(s[len-1]=='(') return 0;
    if(iso(s[0])||iso(s[len-1])) return 0;
    for(int i=1;i<len;i++)
    {
        //cout<<s[i];
        if(isc(s[i])&&isc(s[i-1])) return 0;//  aa

        if(iso(s[i])&&iso(s[i-1])) return 0;//   ++

        if(s[i-1]=='('&&iso(s[i])) return 0;//  (+

        if(iso(s[i-1])&&s[i]==')') return 0;//   +)

        if(s[i-1]==')'&&isc(s[i])) return 0;//  )a

        if(isc(s[i-1])&&s[i]=='(')return 0;//  a(

        if(s[i-1]=='('&&s[i]==')') return 0;

        if(s[i-1]==')'&&s[i]=='(') return 0;



    }


    int num=0;//()
    for(int i=0;i<len;i++)
    {
        if(s[i]=='(') num--;
        else if(s[i]==')') num++;

        if(num>0) return 0;//   (  ))
    }
    if(num!=0) return 0;//   (( )

    return 1;
}

bool ch2(char s[],int len)
{
    if(len==1) return 1;

    int op=0;
    int h=0;
    for(int i=0;i<len;i++)
        if(iso(s[i])) op++;

    stack<char>st;
    for(int i=0;i<len;i++)
    {
        if(isc(s[i])) continue;

        if(s[i]=='('||iso(s[i])) st.push(s[i]);
        else
        {
            int op2=0;
            while(st.size())
            {
                char c=st.top();
                st.pop();

                if(iso(c)) op2++;
                else
                {
                    break;
                }
            }
            if(op2!=1) return 0;
            else h++;
        }

    }

    return h==op-1;
}

int main()
{
    //FAST_IO;
    //freopen("input.txt","r",stdin);

    gets(tmp);

    n=strlen(tmp);

    cnt=0;

    for(int i=0;i<n;i++)
    {
        if(tmp[i]!=' ')
        {
            s[cnt++]=tmp[i];
        }
    }
    s[cnt]='\0';

    n=cnt;

    //cout<<s<<endl;

    if(!ch1(s,n))
    {
        cout<<"error"<<endl;
    }
    else
    {
        if(ch2(s,n))
        {
            cout<<"proper"<<endl;
        }
        else cout<<"improper"<<endl;
    }


    return 0;

}