403057: GYM100985 H MaratonIME goes to the movies

H. MaratonIME goes to the moviestime limit per test4 secondsmemory limit per test128 megabytesinputstandard inputoutputstandard outputBetter than "Fifth Wave"in the World, Everyone

Believe it if you can, studies show that we in MaratonIME live not only out of competitive programming.

In a saturday, after taking part in a virtual contest, our heroes decide to enjoy the afternoon watching a movie session. But they didn't choose any movie, but an n-D movie, that is, a movie with n dimensions.

During a chase scene, the main character jumps over a chain in the parking lot. Of course this was done in a very athletic way, and for some reason that drove Yan, one of the competitive programmers, mad.

"Hollywood makes everything seem easy, but jumping over a chain is really hard!"

The rest of the crowd, after the movie, argued with Yan that the actor surely jumped over the chain, but Yan disagreed, saying that it was done by some camera trick or by special effects.

To prove his point, he bought another ticket for the movie and this time he took highly precise measuring instruments to the session. Yan's plan was to show that the distance from the actor's foot to the floor was smaller than the distance from the chain to the floor, and that would prove that the actor didn't actually jump over the chain.

But math in n dimensions is hard. Everyone knows that distance in the 2D plane between two points (x₀, y₀) and (x₁, y₁) is given by the formula

Most people also know that distance between two points (x₀, y₀, z₀) e (x₁, y₁, z₁) in 3D space is given by the formula

Both formulas describe the euclidean distance, in the 2 and 3 dimensional case. Your task is, given three points in an n dimensional space, tell if the the closest ones are the foot and the floor or the chain and the flooor, according to euclidean distance.

Input

The input begins with an integer n, followed by three lines, each with the representation of a point in an n-dimensional space.

Dimensions confuse us, humans, so you can assume that 1 ≤ n ≤ 10⁵.

The second line represents the coordinates of the floor, and contains n integers a₁, ..., a_n.

The third line represents the coordinates of the foot of the main character, and contains n integers b₁, ..., b_n.

The fourth line represents the coordinates of the chain, and contains n integers c₁, ..., c_n.

The movie theather is not arbitrarily large, so you can assume that the absolute value of these coordinates are not greater than 10⁴.

Output

Print who wins the argument, that is, print "Yan" if the distance between the floor and the foot is not greater than the distance between the floor and the chain, or "MaratonIME" otherwise.

ExamplesInput

2
0 0
1 1
2 2

Output

Yan

Input

4
0 0 0 0
2 2 2 2
1 1 1 1

Output

MaratonIME