Isomorphic Strings

Given two strings s and t, determine if they are isomorphic.

Two strings s and t are isomorphic if the characters in s can be replaced to get t.

All occurrences of a character must be replaced with another character while preserving the order of characters. No two characters may map to the same character, but a character may map to itself.

Example:

Input

s = "egg", t = "add"

Output

true

Input

s = "foo", t = "bar"

Output

false

Input

s = "paper", t = "title"

Output

true