Maggu and Maggie likes to play a simple card game. Game goes this way: Given n cards each containing a number.In one go, any one of them picks up one card from the n cards and then second one picks up one card from the remaining cards. The card holder having card containing greater number will win the game.

Rather than playing game ,maggu thinks of calculating his winning or loosing probability. Help him as he is not good at mathematics.

NOTE: A game is only lost by a player when it is won by other player .

INPUT:
first line of input contains a single integer n denoting the number of cards.Next line of input contains n space separated integers denoting number on each card.

OUTPUT:
output consists of one line only containing two space separated real numbers denoting the winning and loosing probability of maggu.

CONSTRAINTS:
n<=10^6
A[i]<=10^6