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: Accepted)

import sys
input = sys.stdin.readline

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))

compression_dict={a: ind+1 for ind, a in enumerate(sorted(set(A)|set(B)))}

SA=sorted(A)
SB=sorted(B)

for i in range(N):
    if SA[i]>SB[i]:
        print("No")
        sys.exit()

for i in range(N-1):
    if SB[i]>=SA[i+1]:
        print("Yes")
        sys.exit()

AB=[(B[i],A[i]) for i in range(N)]
AB.sort()

DICT={a:ind for ind,a  in enumerate(SA)}

Group=[i for i in range(N)]# グループ分け.Group[i]=jのときiとjは同じグループ

def find(x):# find(a)=find(b)のとき同じグループ
    while Group[x] != x:
        x=Group[x]
    return x

def Union(x,y):  # xとyが同じグループになるよう更新
    if find(x) != find(y):
        Group[find(y)]=Group[find(x)]=min(find(y),find(x))

for i in range(N):
    _,a=AB[i]

    Union(DICT[a],i)

if len(set([find(i) for i in range(N)]))==1:
    print("No")
else:
    print("Yes")