SOLVE

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Simple Game

Problem

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Monk and !Monk decided to play a simple number game. Each of them had a set of numbers (may contain a number more than once) to play with. Lets denote by $$A[]$$ the set belonging to Monk, and by $$B[]$$, the set belonging to !Monk.

They defined three functions $$f(x)$$ , $$g(x)$$ and $$V(x)$$ :

$$f(x)$$ : Returns count of numbers strictly smaller than $$x$$ in opponent's set

$$g(x)$$ : Returns count of numbers strictly greater than $$x$$ in opponent's set

$$V(x)$$ : $$f(x) \times g(x)$$

Score of a player is defined to be the $$ \sum_ {} V(x) $$ for each element $$x$$ present in the players set.

The player with **$$higher$$** score wins the game.

**Input**:

- The first line contains two positive integers N and M where N and M represent the number of elements present in Monk and !Monk's sets respectively.
- The second line contains N space separated integers - elements present in Monk's set
- The third line contains M space separated integers - elements present in !Monk's set

**Output**:

- If Monk wins, print "Monk" (without quotes) followed by a space and the score difference between him and !Monk
- If !Monk wins, print "!Monk" (without quotes) followed by a space and the score difference between him and Monk
- If both players have equal scores, then print "Tie" (without quotes).

**Constraints**:

$$ 1 \le N,M \le 10^5 $$

$$ 0 \le A[i],B[i] \le 10^9 $$

Explanation

*Monk's Set* : {1,3}

*!Monk's Set* : {0,5}

*Score of Monk* :

```
f(1) = 1, There is one element {0}
f(3) = 1, There is one element {0}
g(1) = 1, There is one element {5}
g(3) = 1, There is one element {5}
Score = f(1) * g(1) + f(3) * g(3) = 1 + 1 = 2
```

*Score of !Monk* :

```
f(0) = 0, There are no elements smaller than 0 with Monk
f(5) = 2, There are two elements {1,3}
g(0) = 2, There are two elements {1,3}
g(5) = 0, There are no elements greater than 5 with Monk
Score = f(0) * g(0) + f(5) * g(5) = 0 + 0 = 0
```

```
Score of Monk > Score of !Monk
```

Difference = 2 - 0 = 2
Time Limit:
1.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

Marking Scheme:
Marks are awarded when all the testcases pass.

Allowed Languages:
C,
C++,
Clojure,
C#,
D,
Erlang,
F#,
Go,
Groovy,
Haskell,
Java,
Java 8,
JavaScript(Rhino),
JavaScript(Node.js),
Lisp,
Lisp (SBCL),
Lua,
Objective-C,
OCaml,
Octave,
Pascal,
Perl,
PHP,
Python,
Python 3,
R(RScript),
Racket,
Ruby,
Rust,
Scala 2.11.8,
Swift,
Visual Basic

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OTHER PROBLEMS OF THIS CHALLENGE

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