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Ishaan And Sticks

Ishaan has a craving for sticks. He has N sticks. He observes that some of his sticks are of the same length, and thus he can make squares out of those. He wants to know how big a square he can make using those sticks as sides. Since the number of sticks is large, he can't do that manually. Can you tell him the maximum area of the biggest square that can be formed? Also, calculate how many such squares can be made using the sticks.

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Ishaan And Sticks

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Ishaan has a craving for sticks. He has N sticks. He observes that some of his sticks are of the same length, and thus he can make squares out of those. He wants to know how big a square he can make using those sticks as sides. Since the number of sticks is large, he can't do that manually. Can you tell him the maximum area of the biggest square that can be formed? Also, calculate how many such squares can be made using the sticks.

Constraints

1 <= N <= 10^5 1 <= arr[i] <= 10^3

Format

Input

Input is managed for you

Output

Output is managed for you

Example

Sample Input

10 3 3 4 4 3 4 3 1 4 2

Sample Output

16 1

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