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)

#%%
n = int(input())
aa = list(map(int, input().split()))
bb = list(map(int, input().split()))

a = aa.copy()
b = bb.copy()

a.sort()
b.sort()

flag = False
for i in range(n):
    if a[i] <= b[i]:
        pass
    else:
        flag = True



c = [0] * n
d = [0] * n
for i in range(n):
    c[i] = [aa[i], i]

c.sort()
for i in range(n):
    d[i] = c[i][1]

#print(d)

check = [0] * n
st = d[0]
for i in range(n):
    tmp = d[st]
    check[tmp] = 1
    st = tmp

#print(check)
flag2 = True
for i in range(n):
    if check[i] == 0:
        flag2 = False
    else:
        flag2 = True

if flag or flag2:
    print('No')
else:
    print('Yes')