Practice Conditions with the exercise "The Dart 101"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Conditions

Statement

Goal

Everybody knows the dart game 101. But this times the rules have changed.

Every player shoot 3 darts a round, unless you reach or exceed 101 points, in which case your round immediately ends.

When a dart hits the target you tentatively collect points. There are multiplier rings that increase the points of some darts.
For example :
When you touch the 19, your total is increased by 19.
When you touch the double 19 (2*19) , your total is increased by 2*19=38.
When you touch the triple 19 (3*19), your total is increased by 3*19=57.

Each time you miss the target, your total is decreased by 20 points.
If you miss twice consecutively in the same round, your total is decreased by another 10 points.
If you miss three times in the same round, your whole total is reset at 0.
In other words X.X means -40 but XX. and .XX means -50 in the same round.

To win, you must score exactly 101 points.

If you exceed the score of 101 after a shoot, you revert to your total before your current round and your round ends here. Your round may therefore end before your third shoot.

The player who has reached 101 in the fewest rounds wins the game.
You have to print the winner's name.

Example of calculation :
10 5 3*18 20 X 2*14 17 4
In the round 1, the player scores 10 + 5 + 3*18 = 10 + 5 + 54 = 69 points
In the round 2, the player scores 20 - 20 + 28 = 28 points. The total is 69 + 28 = 97 points
In the round 3, the player cannot score 17. The total stays at 97 points.
In the round 4, the player scores 4 points and reaches exactly 101.
This player finishes in 4 rounds.

Input

Line1 : A number N of player
Next N lines : name of player
Next N lines : shoots of a player separated with space (X when a player missed the target).

Output

Line 1 : The name of the winner

Constraints

1 ≤ N ≤ 8

Example

Input

2
Hugo
Guillaume
10 5 3*18 15 5 4 8
5 5 10 2*19 5 6 2*5 1 20 1

Output

Hugo

Solve it

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