time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Let $a$ and $b$ be some non-negative integers. Let's define strange addition of $a$ and $b$ as following:

1. write down the numbers one under another and align them by their least significant digit;
2. add them up digit by digit and concatenate the respective sums together.

Assume that both numbers have an infinite number of leading zeros.

For example, let's take a look at a strange addition of numbers $3248$ and $908$:

You are given a string $c$, consisting of $n$ digits from $0$ to $9$. You are also given $m$ updates of form:

• $x~d$ — replace the digit at the $x$-th position of $c$ with a digit $d$.

Note that string $c$ might have leading zeros at any point of time.

After each update print the number of pairs $(a, b)$ such that both $a$ and $b$ are non-negative integers and the result of a strange addition of $a$ and $b$ is equal to $c$.

Note that the numbers of pairs can be quite large, so print them modulo $998244353$.

Input

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 5 \cdot 10^5$) — the length of the number $c$ and the number of updates.

The second line contains a string $c$, consisting of exactly $n$ digits from $0$ to $9$.

Each of the next $m$ lines contains two integers $x$ and $d$ ($1 \le x \le n$, $0 \le d \le 9$) — the descriptions of updates.

Output

Print $m$ integers — the $i$-th value should be equal to the number of pairs $(a, b)$ such that both $a$ and $b$ are non-negative integers and the result of a strange addition of $a$ and $b$ is equal to $c$ after $i$ updates are applied.

Note that the numbers of pairs can be quite large, so print them modulo $998244353$.

Example
Input
2 3
14
2 4
2 1
1 0

Output
15
12
2

Note

After the first update $c$ is equal to $14$. The pairs that sum up to $14$ are: $(0, 14)$, $(1, 13)$, $(2, 12)$, $(3, 11)$, $(4, 10)$, $(5, 9)$, $(6, 8)$, $(7, 7)$, $(8, 6)$, $(9, 5)$, $(10, 4)$, $(11, 3)$, $(12, 2)$, $(13, 1)$, $(14, 0)$.

After the second update $c$ is equal to $11$.

After the third update $c$ is equal to $01$.