Mahjong Hands

Mahjong is a game played with tiles. Each tile is numbered from 1 to 9, and belongs to one of three suits, PIN, BAMBOO, or CHARACTER. There are 4 tiles for each number and suit combination (so $9 \times 3 \times 4 = 108$ tiles in total).

Tiles of the same suit can be formed into tile groups. Three tiles of the same suit and number is called a SET. Three tiles of the same suit in consecutive numbering is called a STRAIGHT. For example, three tiles of the PIN suit with the numbers 4, 5, 6 would be a valid tile group because it is a STRAIGHT.

When forming tile groups, the same tile cannot be used in more than one tile group. For example, four tiles of the PIN suit with the numbers 4, 5, 6, 7 would not count as two tile groups, but can only be formed into one tile group with one tile remaining unused.

A Mahjong hand contains 14 tiles. A hand is COMPLETE if the tiles can be formed into 4 tile groups as well as a remaining pair of identical tiles (that is, they have the same suit and number). However, to win a game of Mahjong, your hand must not only be COMPLETE, but must also satisfy a win condition. A Mahjong hand is SIMPLE if it contains no tiles numbered 1 and no tiles numbered 9. You win if your hand is both COMPLETE and SIMPLE.

Your job is to figure out whether a Mahjong hand is COMPLETE or SIMPLE or both.

Input

The first line will contain three space-separated integers, the number of PIN, BAMBOO, and CHARACTER tiles. The total number of tiles will always be equal to 14.

The second line will contain a sorted list of space-separated integers denoting the numbers on the PIN tiles.

The third line will contain a sorted list of space-separated integers denoting the numbers on the BAMBOO tiles.

The fourth line will contain a sorted list of space-separated integers denoting the numbers on the CHARACTER tiles.

Each list of tile numbers will appear in sorted order.

Output

Print out:

• WIN if the hand is simple and also complete.
• COMPLETE if the hand is complete but not simple.
• SIMPLE if the hand is simple but not complete.
• SAD if the hand is not simple or complete.

Subtasks

• Subtask 1 (10%): No tiles have the same suit and number.
• Subtask 2 (20%): Each suit contains 3 tiles numbered 1, with the remaining 5 tiles being numbered 2.
• Subtask 3 (30%): There are only 2 tiles in the PIN suit and they are the same number. Also, there are at most 9 tiles in a suit.
• Subtask 4 (40%): No constraints.

Explanation

In sample case 1, the PIN tiles form a straight (2, 3, 4) and the CHARACTER tiles form three SETs (2, 2, 2 and 3, 3, 3 and 4, 4, 4) and a pair (5, 5) which means the hand is COMPLETE. Since there are no tiles numbered 1 or 9, the hand is also SIMPLE. Since the hand is COMPLETE and SIMPLE, we WIN.

Alternatively, the CHARACTER tiles could form three STRAIGHTs instead of three SETs (2, 3, 4 and 2, 3, 4 and 2, 3, 4).

In sample case 2, it is impossible to form 4 tile groups with a remaining pair of identical tiles. The hand is also not SIMPLE as there are tiles numbered 1 (in the PIN suit).