1499_E. Chaotic Merge_21657
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: 

  * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; 
  * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. 



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 ∑ _{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

Input


aaa
bb


Output


24


Input


code
forces


Output


1574


Input


aaaaa
aaa


Output


0


Input


justamassivetesttocheck
howwellyouhandlemodulooperations


Output


667387032

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.
import java.util.*;
import java.util.Map.Entry;

import java.math.*;
import java.io.*;

public class Main {
	static final int mod = 998244353;

	public static void main(String[] args) throws FileNotFoundException {
		InputReader in = new InputReader(System.in);
		// Scanner in = new Scanner(System.in);
		// Scanner in = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));
		PrintWriter out = new PrintWriter(System.out);
		// InputReader in = new InputReader(new
		// File("ethan_traverses_a_tree.txt"));
		// PrintWriter out = new PrintWriter(new
		// File("ethan_traverses_a_tree-output.txt"));

		String s1 = in.next();
		String s2 = in.next();

		char[] a = s1.toCharArray();
		char[] b = s2.toCharArray();

		int n = a.length;
		int m = b.length;

		int[] singlecounta = getsinglecount(a);
		int[] singlecountb = getsinglecount(b);

		int ans = 0;
		int[][][] dp = new int[n + 1][m + 1][2];
		for (int i = n - 1; i >= 0; i--) {
			for (int j = m - 1; j >= 0; j--) {
				// a first
				int suma = 0;
				if (i == n - 1) {
					if (a[i] != b[j]) {
						suma = (suma + singlecountb[j]) % mod;
					}
				} else {
					if (a[i] != a[i + 1]) {
						suma = (suma + dp[i + 1][j][0]) % mod;
					}
					if (a[i] != b[j]) {
						suma = (suma + dp[i + 1][j][1]) % mod;
						suma = (suma + singlecountb[j]) % mod;
					}
				}
				dp[i][j][0] = suma;
				// b first
				int sumb = 0;
				if (j == m - 1) {
					if (b[j] != a[i]) {
						sumb = (sumb + singlecounta[i]) % mod;
					}
				} else {
					if (b[j] != b[j + 1]) {
						sumb = (sumb + dp[i][j + 1][1]) % mod;
					}
					if (b[j] != a[i]) {
						sumb = (sumb + dp[i][j + 1][0]) % mod;
						sumb = (sumb + singlecounta[i]) % mod;
					}
				}
				dp[i][j][1] = sumb;

				ans = (ans + dp[i][j][0]) % mod;
				ans = (ans + dp[i][j][1]) % mod;
			}
		}

		out.printf("%d\n", ans);

		out.close();
	}

	public static int[] getsinglecount(char[] a) {
		int n = a.length;
		int[] singlecount = new int[n];

		for (int i = n - 1; i >= 0; i--) {
			if (i == n - 1) {
				singlecount[i] = 1;
			} else {
				if (a[i] == a[i + 1]) {
					singlecount[i] = 1;
				} else {
					singlecount[i] = (singlecount[i + 1] + 1) % mod;
				}
			}
		}

		return singlecount;
	}

	static class InputReader {
		BufferedReader br;
		StringTokenizer st;

		public InputReader(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public InputReader(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		public boolean hasNext() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return false;
				st = new StringTokenizer(s);
			}
			return true;
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}