As an experiment the Educational Codeforces Round 33 will be rated for Div. 2.
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A. Is it rated?

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIs it rated?

Here it is. The Ultimate Question of Competitive Programming, Codeforces, and Everything. And you are here to answer it.

Another Codeforces round has been conducted. No two participants have the same number of points. For each participant, from the top to the bottom of the standings, their rating before and after the round is known.

It's known that if at least one participant's rating has changed, then the round was rated for sure.

It's also known that if the round was rated and a participant with lower rating took a better place in the standings than a participant with higher rating, then at least one round participant's rating has changed.

In this problem, you should not make any other assumptions about the rating system.

Determine if the current round is rated, unrated, or it's impossible to determine whether it is rated of not.

Input

The first line contains a single integer *n* (2 ≤ *n* ≤ 1000) — the number of round participants.

Each of the next *n* lines contains two integers *a*_{i} and *b*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ 4126) — the rating of the *i*-th participant before and after the round, respectively. The participants are listed in order from the top to the bottom of the standings.

Output

If the round is rated for sure, print "rated". If the round is unrated for sure, print "unrated". If it's impossible to determine whether the round is rated or not, print "maybe".

Examples

Input

6

3060 3060

2194 2194

2876 2903

2624 2624

3007 2991

2884 2884

Output

rated

Input

4

1500 1500

1300 1300

1200 1200

1400 1400

Output

unrated

Input

5

3123 3123

2777 2777

2246 2246

2246 2246

1699 1699

Output

maybe

Note

In the first example, the ratings of the participants in the third and fifth places have changed, therefore, the round was rated.

In the second example, no one's rating has changed, but the participant in the second place has lower rating than the participant in the fourth place. Therefore, if the round was rated, someone's rating would've changed for sure.

In the third example, no one's rating has changed, and the participants took places in non-increasing order of their rating. Therefore, it's impossible to determine whether the round is rated or not.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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