Problem: After the fourth season Sherlock and Moriary have realized the whole foolishness of the battle between them and decided to continue their competitions in peaceful game of Credit Cards.

Rules of this game are simple: each player bring his favourite n-digit credit card. Then both players name the digits written on their cards one by one. If two digits are not equal, then the player, whose digit is smaller gets a flick (knock in the forehead usually made with a forefinger) from the other player. For example, if n = 3, Sherlock's card is 123 and Moriarty's card has number 321, first Sherlock names 1 and Moriarty names 3 so Sherlock gets a flick. Then they both digit 2 so no one gets a flick. Finally, Sherlock names 3, while Moriarty names 1 and gets a flick.

Of course, Sherlock will play honestly naming digits one by one in the order they are given, while Moriary, as a true villain, plans to cheat. He is going to name his digits in some other order (however, he is not going to change the overall number of occurences of each digit). For example, in case above Moriarty could name 1, 2, 3 and get no flicks at all, or he can name 2, 3 and 1 to give Sherlock two flicks.

Your goal is to find out the minimum possible number of flicks Moriarty will get (no one likes flicks) and the maximum possible number of flicks Sherlock can get from Moriarty. Note, that these two goals are different and the optimal result may be obtained by using different strategies.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the number of digits in the cards Sherlock and Moriarty are going to use.

The second line contains n digits — Sherlock's credit card number.

The third line contains n digits — Moriarty's credit card number.

Output

First print the minimum possible number of flicks Moriarty will get. Then print the maximum possible number of flicks that Sherlock can get from Moriarty.

Examples

Input

3
123
321


Output

0
2


Input

2
88
00


Output

2
0

Note

First sample is elaborated in the problem statement. In the second sample, there is no way Moriarty can avoid getting two flicks.

Solution (in PYTHON):

Solution:
#!/usr/bin/python

LOG = True
LOG = False

def log(string):
    if LOG:
        print string

def get_minimum_sherlock_flicks(digits, sherlock_card, moriarty_card):
    """
    gets sorted cards.
    O(n)
    """
    log("Getting minimum sherlock flicks for sherlock: {} moriarty: {}".format(sherlock_card,moriarty_card))
    flicks = 0
    sherlock_digit = 0
    moriarty_digit = 0
    while sherlock_digit < digits:
        log("sherlock_digit={}".format(sherlock_card[sherlock_digit]))
        # increment moriarty_digit until reaching a digit greater/equal to sherlock current digit.
        while   (moriarty_digit < digits and
                 moriarty_card[moriarty_digit] < sherlock_card[sherlock_digit]):
            log("moriarty_digit={}".format(moriarty_card[moriarty_digit]))
            moriarty_digit += 1

        if moriarty_digit == digits:
            log("didn't find a good moriarty digit")
            return moriarty_digit - sherlock_digit
        else:
            log("Good moriarty digit is {}".format(moriarty_card[moriarty_digit]))
            
        moriarty_digit += 1
        sherlock_digit += 1

    return moriarty_digit - sherlock_digit
        
def get_maximum_moriarty_flicks(digits, sherlock_card, moriarty_card):
    """
    gets sorted cards.
    O(n)
    """
    log("Getting maximum moriarty flicks for sherlock: {} moriarty: {}".format(sherlock_card,moriarty_card))
    flicks = 0
    sherlock_digit = 0
    moriarty_digit = 0
    while sherlock_digit < digits:
        log("sherlock_digit={}".format(sherlock_card[sherlock_digit]))
        # increment moriarty_digit until reaching a digit greater than sherlock current digit.
        while   (moriarty_digit < digits and
                 moriarty_card[moriarty_digit] <= sherlock_card[sherlock_digit]):
            log("moriarty_digit={}".format(moriarty_card[moriarty_digit]))
            moriarty_digit += 1
            
        if moriarty_digit == digits:
            log("didn't find a good moriarty digit")
            return digits - (moriarty_digit - sherlock_digit)
        else:
            log("Good moriarty digit is {}".format(moriarty_card[moriarty_digit]))
            
        moriarty_digit += 1
        sherlock_digit += 1

    return digits - (moriarty_digit - sherlock_digit)
    
def main():
    digits = int(raw_input())
    sherlock_card = [int(x) for x in raw_input()]
    moriarty_card = [int(x) for x in raw_input()]
    
    # Order doesn't matter.
    # O(nlogn)
    moriarty_card.sort()
    sherlock_card.sort()
    
    # minimum flicks sherlock gives.
    minimum_sherlock_flicks = get_minimum_sherlock_flicks(digits, sherlock_card, moriarty_card)
    log("minimum sherlock flicks is {}".format(minimum_sherlock_flicks))
    
    # maximum flicks moriarty gives.
    maximum_moriarty_flicks = get_maximum_moriarty_flicks(digits, sherlock_card, moriarty_card)
    log("maximum moriarty flicks is {}".format(maximum_moriarty_flicks))
    
    print minimum_sherlock_flicks
    print maximum_moriarty_flicks

if __name__ == "__main__":
    main()