Codeforces Round #313 (Div. 2) D. Equivalent Strings

D. 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 calledequivalent 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

aaba
abaa

output

YES

input

aabb
abab

output

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".

 

题目链接：http://codeforces.com/contest/560/problem/D

 

 题目大意：给两个字符串，判断它们是否相等，相等有两种情况，一个是直接相等，一个是切成长度相同的两份以后两子串交叉相等

 

 题目分析：裸的DFS，按照题意搜就行了，如果当前长度为奇数，直接返回false，否则分两种情况搜

 

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
#define MAX 200100

char a[MAX], b[MAX];

bool dfs(char *p1, char *p2, int len)
{
    if(!strncmp(p1, p2, len))
        return true;
    if(len % 2) 
        return false;
    int n = len / 2;
    if(dfs(p1 ,p2 + n, n) && dfs(p1 + n, p2, n)) 
        return true;
    if(dfs(p1, p2, n) && dfs(p1 + n, p2 + n, n)) 
        return true;
    return false;
}

int main()
{
    scanf("%s %s", a, b);
    printf("%s\n", dfs(a, b, strlen(a)) ? "YES" : "NO");
}