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

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

Solution (in PYTHON3):

Solution:
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.buffer.readline
mod = 998244353
INF = float("inf")


class lazySegTree(object):
	def __init__(self, N):
		self.N = N
		self.LV = (N-1).bit_length()
		self.N0 = 2**self.LV
		self.data = [0]*(2*self.N0) #桁の値を管理(lazy*size)
		self.lazy = [0]*(2*self.N0) #桁の文字を管理
		self.size = [1]*(2*self.N0) #桁の和を管理(10^n)(更新しない)
		for i in range(self.N):
			self.size[self.N0-1+i] = pow(10, self.N-i-1, mod)
		for i in range(self.N0-2, -1, -1):
			self.size[i] = (self.size[2*i+1] + self.size[2*i+2])%mod
	# 遅延セグ木の初期化
	def initialize(self):
		for i in range(self.N):
			self.data[self.N0-1+i] = pow(10, self.N-i-1, mod)
		for i in range(self.N0-2, -1, -1):
			self.data[i] = (self.data[2*i+1] + self.data[2*i+2])%mod

  # 遅延伝播を行うindexを生成
	def gindex(self, l, r):
		L = l + self.N0
		L >>= 1
		R = r + self.N0
		R >>= 1
		if l & 1:
			lc = 0
		else:
			lc = (L & -L).bit_length()
		if r & 1:
			rc = 0
		else:
			rc = (R & -R).bit_length()
		for i in range(self.LV):
			if rc <= i:
				yield R
			if L < R and lc <= i:
				yield L
			L >>= 1 
			R >>= 1

	# 遅延伝搬処理
	def propagates(self, *ids):
		for i in reversed(ids):
			v = self.lazy[i - 1]
			if not v:
				continue
			self.lazy[2*i-1] = v
			self.lazy[2*i] = v
			self.data[2*i-1] = v * self.size[2*i-1]
			self.data[2*i] = v * self.size[2*i]
			self.lazy[i-1] = 0

	def update(self, l, r, x):
		*ids, = self.gindex(l, r+1)
		self.propagates(*ids)
		L = self.N0 + l
		R = self.N0 + r + 1
		while L < R:
			if R & 1:
				R -= 1
				self.lazy[R-1] = x #桁の文字を更新
				self.data[R-1] = x * self.size[R-1] #桁の値を更新
			if L & 1:
				self.lazy[L-1] = x
				self.data[L-1] = x * self.size[L-1]
				L += 1
			L >>= 1
			R >>= 1
		for i in ids:
			self.data[i-1] = (self.data[2*i-1] + self.data[2*i])%mod

	# 区間[l, r]内のdataの和を求める
	def query(self, l, r):
		self.propagates(*self.gindex(l, r+1))
		L = self.N0 + l
		R = self.N0 + r + 1
		s = 0
		while L < R:
			if R & 1:
				R -= 1
				s = (s + self.data[R-1])%mod
			if L & 1:
				s = (s + self.data[L-1])%mod
				L += 1
			L >>= 1
			R >>= 1
		return s

N, Q = map(int, input().split())
lSeg = lazySegTree(N)
lSeg.initialize()

for i in range(Q):
	L, R, D = map(int, input().split())
	L -= 1
	R -= 1
	lSeg.update(L, R, D)
	ans = lSeg.query(0, N-1)
	ans %= mod
	print(ans)