Equal Frequency Tables on a Small Domain

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given two integer arrays $A=(a_1,\ldots,a_n)$ and $B=(b_1,\ldots,b_n)$ whose values lie in $[0,1000]$. For each value $v$, define its frequencies $f_A(v)$ and $f_B(v)$. Determine whether $f_A(v)=f_B(v)$ for every $v$.

Input

Line 1 contains $n$. Line 2 contains $a_1,\ldots,a_n$. Line 3 contains $b_1,\ldots,b_n$.

Output

Print YES if the two frequency tables are equal, otherwise NO.

Subtasks

Subtask 1 (20 points): $1\le n\le 50$; $0\le a_i,b_i\le 100$.

Subtask 2 (30 points): $1\le n\le 5000$; $0\le a_i,b_i\le 500$.

Subtask 3 (50 points): $1\le n\le 100000$; $0\le a_i,b_i\le 1000$.

Example

Input

4
1 2 2 3
2 3 2 1

Output

YES

Explanation

The values follow directly from the definitions and illustrate the valid index range of the array scan.