Check the Check

As a tourist in Paris, you are told to always check the itemized bill (also called the check) that arrives at the end of a meal, the one listing what you ordered and the total price. Such bills are often handwritten, and the waiter adds the total up by hand. You do not want to pay more than your meal costs, so you protest whenever a mistake favors the restaurant. If the restaurant charges you less than it should, you pay without a word.

Write a program that decides whether to pay the total printed on the check or to protest about it.

The input consists of $2n + 2$ lines.

• For every $k$ with $0 \le k \le n - 1$, line $2k + 1$ holds the name $d_k$ of an ordered dish.
• For every $k$ with $0 \le k \le n - 1$, line $2k + 2$ holds the integer price $p_k$ of $d_k$ in euros and the number of orders $c_k$ of $d_k$, separated by one space.
• Line $2n + 1$ holds the word TOTAL.
• Line $2n + 2$ holds the integer total $T$ in euros computed by the waiter.

The value of $n$ is not given in the input. Read dish entries until you reach the line equal to TOTAL.

Limits

• For every $k$ with $0 \le k \le n - 1$:
  • $d_k$ has at most 1000 characters, and is never equal to TOTAL;
  • $0 \le p_k \le 1000$;
  • $0 \le c_k \le 10$;
• $0 \le n \le 100\,000$;
• $T \le 2\,000\,000\,000$.

Print one line. Print PAY if the total $T$ on the check is less than or equal to the real total $\sum_{k=0}^{n-1} p_k c_k$, and PROTEST if it is larger.