Rummikub

Rummikub uses tiles numbered 1 to 13 in four colors, written here as A, B, C, and D. You hold 14 tiles and try to build groups and runs.

A group is 3 or 4 tiles that share a number and have all different colors. A run is 3 or more tiles of one color with consecutive numbers. The score of a combination is the sum of the numbers on its tiles.

Each tile is written as a color letter followed by a number from 1 to 13. A5, B5, C5 is a group, and A5, A6, A7 is a run.

A hand can contain the same tile more than once. A combination is built from distinct tiles, so duplicate copies do not count.

For each hand, decide whether any group or run exists, and if one does, find the combination with the highest score. When several combinations share the highest score, compare their sorted tile lists one tile at a time and take the smaller color letter, or the smaller number when the colors match. If one list is exactly the beginning of the other, take the shorter list.

For example, in A5 B5 C5 A6 A7 B13 A12 C1 C9 D1 D2 D3 D7 D12 the group A5 B5 C5 scores 15, the run A5 A6 A7 scores 18, and the run D1 D2 D3 scores 6, so the answer is A5 A6 A7 with 18 points.

The first line contains the number of data sets $T$. ($1 \le T \le 100$)

Each of the next $T$ lines contains 14 tiles separated by spaces, in random order. Each tile is one of the letters A, B, C, D followed by an integer from 1 to 13.

Print one line for each data set.

If no group and no run exists, print NO GROUPS OR RUNS. Otherwise print the tiles of the highest scoring combination, sorted by color letter and by number within one color, separated by spaces, then print the score of that combination at the end of the same line.