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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

n, q = gets.split.map(&:to_i)

s = [[1, n, "1"]]

q.times do
  l, r, d = gets.split
  l = l.to_i
  r = r.to_i

  arr = []
  flag = true
  s.each do |li, ri, di|
    if ri < l || r < li
      arr << [li, ri, di]
      next
    end
    
    if flag && l <= ri
      arr << [li, l - 1, di] if li < l
      arr << [l, r, d]
      flag = false
    end

    if !flag && r < ri
      arr << [r + 1, ri, di]
    end
  end
  s = arr
  
  puts s.map {|l, r, d| d * (r - l + 1) }.join("").to_i % 998_244_353
end