Problem:
Score : 500 points

Problem Statement

You have a string S of length N.
Initially, all characters in S are 1s.

You will perform queries Q times.
In the i-th query, you are given two integers L_i, R_i and a character D_i (which is a digit).
Then, you must replace all characters from the L_i-th to the R_i-th (inclusive) with D_i.

After each query, read the string S as a decimal integer, and print its value modulo 998,244,353.

Constraints

1 \leq N, Q \leq 200,000

1 \leq L_i \leq R_i \leq N

1 \leq D_i \leq 9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
L_1 R_1 D_1
:
L_Q R_Q D_Q

Output

Print Q lines.
In the i-th line print the value of S after the i-th query, modulo 998,244,353.

Sample Input 1

8 5
3 6 2
1 4 7
3 8 3
2 2 2
4 5 1

Sample Output 1

11222211
77772211
77333333
72333333
72311333

Sample Input 2

200000 1
123 456 7

Sample Output 2

641437905

Don't forget to take the modulo.

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(let* ((n (read))
    (s (make-string n :initial-element #\1))
    (q (read)))
    (loop for i below q do
        (let ((l (read))
            (r (read))
            (dd (read-char)))
            (setq s (concatenate 'string 
                        (subseq s 0 (- l 1))
                        (make-string (+ (- r l) 1) :initial-element dd)
                        (subseq s r n)))
            (format t "~D~%"
                (rem (parse-integer s) 998244353)
            )
        )
    )
)