You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s.
Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order.
A merge z is produced from a sequence a by the following rules:
Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i.
Let's call a string z chaotic if for all i from 2 to |z| z_i-1 ≠ z_i.
Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive.
Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered.
Calculate Σ _1 ≤ l_1 ≤ r_1 ≤ |x| \\ 1 ≤ l_2 ≤ r_2 ≤ |y| f(l_1, r_1, l_2, r_2). Output the answer modulo 998\,244\,353.
Input
The first line contains a string x (1 ≤ |x| ≤ 1000).The second line contains a string y (1 ≤ |y| ≤ 1000).Both strings consist only of lowercase Latin letters.
Output
Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998\,244\,353.
Examples
Note
In the first example there are: 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 · 2 + 3 · 1 + 4 · 1 + 2 · 2 + 2 · 0 + 1 · 1 = 24.