Problem Statement

Two players, Alice and Bob, are going to play a game of claiming territory on a grid.

You are given a grid with $H$ rows and $W$ columns. Here, the top-left cell is $(1, 1)$ and the bottom-right cell is $(H, W)$.

In the initial state, Alice's and Bob's pieces are placed on cells $(X_A, Y_A), (X_B, Y_B)$ ($(X_A,Y_A)\neq(X_B,Y_B)$), respectively.

Also, cell $(X_A, Y_A)$ is Alice's territory, cell $(X_B, Y_B)$ is Bob's territory, and all other cells belong to neither player's territory.

Alice goes first, and the players take turns alternately. On their turn, a player performs the following operations in the order shown.

1. Let $(X, Y)$ be the cell where the player's own piece is currently located. Choose a cell $(X^\prime, Y^\prime)$ that satisfies condition $(*)$ and is either the player's own territory or neither player's territory.

$(*)$ The rectangular region having cell $(X, Y)$ and cell $(X^\prime, Y^\prime)$ as the ends of one of its diagonals contains no cell that is the opponent's territory.
Formally, for all integers $i$, $j$ satisfying $\min(X, X^\prime) \le i \le \max(X, X^\prime)$ , $\min(Y, Y^\prime) \le j \le \max(Y, Y^\prime)$, cell $(i, j)$ is not the opponent's territory.

2. Move the player's own piece to $(X^\prime, Y^\prime)$.
3. Make all cells in the rectangular region specified in $(*)$ the player's own territory.

The game ends when Bob's $10^{100}$-th turn is finished.

At the end of the game, the player with more cells in their territory wins. If both players have the same number of such cells, the game is a draw.

Find the number of tuples of variables $(X_A, Y_A, X_B, Y_B)$, which give the initial positions of the cells, such that Alice wins when both players play optimally.

Since this number can be very large, find it modulo $998,244,353$.

Constraints

• $2 \le H \le 10^9$
• $2 \le W \le 10^9$
• All values given in the input are integers