street is developed as follows:    the main line comprises of 1 tile;    then, at that point, a1 lines follow; every one of these lines contains 1 tile more noteworthy than the past line;    then, at that point, b1 columns follow; every one of these lines contains 1 tile not exactly the past line;    then, at that point, a2 columns

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter19: Probabilistic Dynamic Programming
Section: Chapter Questions
Problem 5RP
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 street is developed as follows: 

 

the main line comprises of 1 tile; 

 

then, at that point, a1 lines follow; every one of these lines contains 1 tile more noteworthy than the past line; 

 

then, at that point, b1 columns follow; every one of these lines contains 1 tile not exactly the past line; 

 

then, at that point, a2 columns follow; every one of these lines contains 1 tile more noteworthy than the past line; 

 

then, at that point, b2 lines follow; every one of these columns contains 1 tile not exactly the past line; 

 

... 

 

then, at that point, a lines follow; every one of these columns contains 1 tile more prominent than the past line; 

 

then, at that point, bn columns follow; every one of these lines contains 1 tile not exactly the past line. 

 

You start from the main tile in the primary line and need to arrive at the last line (any tile of it). From your present tile, you can move to any tile in the following column which contacts your present tile. 

 

Ascertain the number of various ways from the primary line to the last line. Since it tends to be enormous, print it modulo 998244353. 

 

Input 

 

The main line contains one integer n (1≤n≤1000). 

 

Then, at that point, n lines follow. The I-th of them contains two integers computer based intelligence and bi (1≤ai,bi≤105; |ai−bi|≤5). 

 

Extra limitation on the input: the succession of artificial intelligence and bi never brings about a line with non-positive number of tiles. 

 

Output 

 

Print one integer — the number of ways from the main line to the last line, taken modulo 998244353.

 

 

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