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 Python (3.4.3) (judge verdict: Wrong Answer)

#!/usr/bin/env python3
import sys
import math
YES = "Yes"  # type: str
NO = "No"  # type: str


def solve(N: int, A: "List[int]", B: "List[int]"):
    if max(B)<max(A):
        print(NO)
        return
    
    ## 完成形を作る
    B_tuple = []
    A_tuple = []
    for i in range(N):
        B_tuple.append((B[i],i))
        A_tuple.append((A[i],i))
    
    A_tuple.sort(key=lambda x: x[0])
    B_tuple.sort(key=lambda x: x[0])
    dif = 0
    for i in range(N):
        dif += abs(A_tuple[i][1]-B_tuple[i][1])
    
    if math.ceil(dif/2) <= N:
        print(YES)
    else:
        print(NO)

    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    B = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    solve(N, A, B)

if __name__ == '__main__':
    main()