Winni is playing a card game with herself since she lost all of her friends when travelling to outer space. Winni lays cards face up on the table. Each card has a non-unique number on it from
to
. Winni proceeds to pick up
cards from the table one at a time. Whenever Winni picks up a card, she receives
dollars where
is the number of cards with the same number that she has already picked up. Can you help Winni determine the maximum amount of money she can obtain?
Input Specification
The first line of input contains integers,
,
,
.
The next line of input contains integers between
to
, representing the number of the cards on the table.
Output Specification
Output the maximum amount of money she can obtain.
Constraints
Subtask 1 [10%]
Subtask 2 [20%]
Subtask 3 [30%]
Subtask 4 [40%]
No additional constraints.
Sample Input
7 10 5
10 8 9 10 9 9 10
Sample Output
4
Explanation For Sample
- She can initially pick up
10
gainingdollars.
- She picks up
9
, gainingdollars.
- She then picks up
10
, gainingdollar.
- She picks up
10
again, gainingdollars.
- She picks up
9
again, gainingdollar.
In total, she gains dollars, which is the maximum amount of money Winni can obtain.
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