Replace Digits

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.

Examples

Input

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

Output

11222211 77772211 77333333 72333333 72311333

Input

200000 1 123 456 7

Output

641437905

inputFormat

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

outputFormat

Output

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

Examples

Input

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

Output

11222211 77772211 77333333 72333333 72311333

Input

200000 1 123 456 7

Output

641437905

样例

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

11222211
77772211
77333333
72333333
72311333

</p>