B. Equivalent Strings

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Today on a lecture about strings Gerald learned a new definition of string equivalency. Two strings a and b of equal length are called equivalent in one of the two cases:

  1. They are equal.
  2. If we split string a into two halves of the same size a1 and a2, and string b into two halves of the same size b1 and b2, then one of the following is correct:
    1. a1 is equivalent to b1, and a2 is equivalent to b2
    2. a1 is equivalent to b2, and a2 is equivalent to b1

As a home task, the teacher gave two strings to his students and asked to determine if they are equivalent.

Gerald has already completed this home task. Now it's your turn!

Input

The first two lines of the input contain two strings given by the teacher. Each of them has the length from 1 to 200 000 and consists of lowercase English letters. The strings have the same length.

Output

Print "YES" (without the quotes), if these two strings are equivalent, and "NO" (without the quotes) otherwise.

Examples

input

Copy

aaba
abaa

output

Copy

YES

input

Copy

aabb
abab

output

Copy

NO

Note

In the first sample you should split the first string into strings "aa" and "ba", the second one — into strings "ab" and "aa". "aa" is equivalent to "aa"; "ab" is equivalent to "ba" as "ab" = "a" + "b", "ba" = "b" + "a".

In the second sample the first string can be splitted into strings "aa" and "bb", that are equivalent only to themselves. That's why string "aabb" is equivalent only to itself and to string "bbaa".

题意：

给你两个字符串，给出字符串相同的定义 ，问你两个字符串是否相等。

#include<iostream>
#include<string>
using namespace std;
bool dfs(string a,string b,int len){
	if(a==b) return true;          //a,b相等 
	if(len&1) return false;       //a,b不相等，并且a,b的长度为奇数，a,b不可能再划分成等同 
	int n=len>>1;
	if(dfs(a.substr(0,n),b.substr(n,n),n)&&dfs(a.substr(n,n),b.substr(0,n),n))  
	//a的前半部分与b的后半部分，&& a的后半部分与b的前半部分 
	return true;
	
	if(dfs(a.substr(0,n),b.substr(0,n),n)&&dfs(a.substr(n,n),b.substr(n,n),n))  
	//a的前半部分和b的前半部分，&& a的后半部分与b的后半部分 
	return true;
	return false;
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	string a,b;
	while(cin>>a>>b){
		if(dfs(a,b,a.length()))
		cout<<"YES"<<endl;
		else 
		cout<<"NO"<<endl;
	}
	return 0;
}