Chess Tournament 2

Task

You want to organize a chess tournament in your town but given the recent developments in the chess world, you want to use some extra measures to make sure that everyone playing there is playing fairly.

Thus, you came up with a system to decide the strength of each move played by each player and in order to decide whether a player cheated or not, you decided to compute the average move strength and if it exceeded a certain threshold based on that player's initial chess rating, then you conclude that a player cheated.

More formally, you are given the data from $t$ chess players. For each chess player you know the number of moves they made during the contest, as well as the initial elo and the threshold you are going to use.

Based on the rules described in the statement, decide whether each player cheated or not.

Input

The first line of the input will contain $t$, the number of players which played in the tournament.

The first line of each test case will contain $\text{n}$, $\text{elo}$ and $\text{threshold}$, representing the number of moves the $i^{th}$ player made during the tournament, the initial rating the player had and the threshold you are going to use for this player.

The second line of each test case will contain $n$ values, representing the strengths of the moves the player did.

Output

The output f will contain for each player a message, namely "Cheater" if the player cheated or "Innocent" otherwise (without the quoting marks).

Restrictions

• $1 \leq t \leq 100$
• $1 \leq n, threshold \leq 1 \ 000$
• $1 \leq elo \leq 3 \ 500$
• $1 \leq strength[i] \leq 5 \ 000$

Example

stdin

3
5 800 400
900 1000 1500 1300 1400
8 1000 200
950 800 1000 1100 1200 845 100 924
6 2500 400
1900 2100 950 2500 2000 3000

stdout

Cheater
Innocent
Innocent

Explanation

The first player's move strength is $6100$ / $5$ = $1220$, which is greater than $1200$, the maximum threshold allowed.

The other two players have not cheated, thus they are innocent.