Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as BS
import Data.Maybe (fromJust)
import Data.List

main :: IO ()
main = do
    n <- readLn :: IO Int
    a <- map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    b <- map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    let a' = sort a
        b' = sort b
        check = and $ zipWith (<=) a' b'
        ab = zip a b
        ab' = zip a' b'
        cnt = sum [ 1 | x <- ab, x `notElem` ab']
    putStrLn $ if check && cnt <= 6 then "Yes" else "No"