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:
class LazySegmentTree():
  def __init__(self, n, op, e, mapping, composition, id):
    self.n = n
    self.op = op
    self.e = e
    self.mapping = mapping
    self.composition = composition
    self.id = id
    self.log = (n - 1).bit_length()
    self.size = 1 << self.log
    self.data = [e] * (2 * self.size)
    self.lazy = [id] * (self.size)

  def update(self, k):
    self.data[k] = self.op(self.data[2 * k], self.data[2 * k + 1])

  def all_apply(self, k, f):
    self.data[k] = self.mapping(f, self.data[k])
    if k < self.size:
      self.lazy[k] = self.composition(f, self.lazy[k])

  def push(self, k): # 親の遅延配列の値を子に反映させる
    self.all_apply(2 * k, self.lazy[k])
    self.all_apply(2 * k + 1, self.lazy[k])
    self.lazy[k] = self.id

  def build(self, arr):
    #assert len(arr) == self.n
    for i, a in enumerate(arr):
      self.data[self.size + i] = a
    for i in range(self.size-1,0,-1):
      self.update(i)

  def set(self, p, x):
    #assert 0 <= p < self.n
    p += self.size
    #事前に関係のある遅延配列を全て反映させてしまう
    for i in range(self.log, 0, -1):
      self.push(p >> i)
    self.data[p] = x #値を更新する
    #関係のある区間の値も更新する
    for i in range(1, self.log + 1):
      self.update(p >> i)

  def get(self, p):
    #assert 0 <= p < self.n
    p += self.size
    #関係のある遅延配列を全て反映させる
    for i in range(1, self.log + 1):
      self.push(p >> i)
    return self.data[p]

  def prod(self, l, r):
    #assert 0 <= l <= r <= self.n
    if l == r: return self.e
    l += self.size
    r += self.size
    for i in range(self.log, 0, -1):
      if ((l >> i) << i) != l: self.push(l >> i)
      if ((r >> i) << i) != r: self.push(r >> i)
    sml = smr = self.e
    while l < r:
      if l & 1:
        sml = self.op(sml, self.data[l])
        l += 1
      if r & 1:
        r -= 1
        smr = self.op(self.data[r], smr)
      l >>= 1
      r >>= 1
    return self.op(sml, smr)

  def all_prod(self):
    return self.data[1]

  def apply(self, p, f):
    #assert 0 <= p < self.n
    p += self.size
    for i in range(self.log, 0, -1):
      self.push(p >> i)
    self.data[p] = self.mapping(f, self.data[p])
    for i in range(1, self.log + 1):
      self.update(p >> i)

  def range_apply(self, l, r, f):
    #assert 0 <= l <= r <= self.n
    if l == r: return
    l += self.size
    r += self.size
    for i in range(self.log, 0, -1):
      if ((l >> i) << i) != l: self.push(l >> i)
      if ((r >> i) << i) != r: self.push((r - 1) >> i)
    l2 = l
    r2 = r
    while l < r:
      if l & 1:
        self.all_apply(l, f)
        l += 1
      if r & 1:
        r -= 1
        self.all_apply(r, f)
      l >>= 1
      r >>= 1
    l = l2
    r = r2
    for i in range(1, self.log + 1):
      if ((l >> i) << i) != l: self.update(l >> i)
      if ((r >> i) << i) != r: self.update((r - 1) >> i)

  def max_right(self, l, g):
    #assert 0 <= l <= self.n
    #assert g(self.e)
    if l == self.n: return self.n
    l += self.size
    for i in range(self.log, 0, -1):
      self.push(l >> i)
    sm = self.e
    while True:
      while l % 2 == 0: l >>= 1
      if not g(self.op(sm, self.data[l])):
        while l < self.size:
          self.push(l)
          l = 2 * l
          if g(self.op(sm, self.data[l])):
            sm = self.op(sm, self.data[l])
            l += 1
        return l - self.size
      sm = self.op(sm, self.data[l])
      l += 1
      if (l & -l) == l: return self.n

  def min_left(self, r, g):
    #assert 0 <= r <= self.n
    #assert g(self.e)
    if r == 0: return 0
    r += self.size
    for i in range(self.log, 0, -1):
      self.push((r - 1) >> i)
    sm = self.e
    while True:
      r -= 1
      while r > 1 and r % 2: r >>= 1
      if not g(self.op(self.data[r], sm)):
        while r < self.size:
          self.push(r)
          r = 2 * r + 1
          if g(self.op(self.data[r], sm)):
            sm = self.op(self.data[r], sm)
            r -= 1
        return r + 1 - self.size
      sm = self.op(self.data[r], sm)
      if (r & -r) == r: return 0

import sys
input = sys.stdin.buffer.readline

INF = pow(10,18)
MOD = 998244353
po32 = pow(2,32)

N, Q = map(int, input().split())

def op(x, y):
  xv, xr = divmod(x,po32)
  yv, yr = divmod(y,po32)
  return ((xv + yv) % MOD)*po32 + (xr + yr) % MOD

def mapping(p, x): #pが更新後の値, xが更新する前の値
  xv, xr = divmod(x,po32)
  if p != INF:
    return (p * xr % MOD)*po32 + xr
  return x

def composition(p, q):
  if p != INF:
    return p
  return q

lis = [1] * (N)
for i in range(N-1,0,-1):
  lis[i - 1] = lis[i] * 10 % MOD

arr = [e*po32+e for e in lis]

e = 0
id = INF

lst = LazySegmentTree(N, op, e, mapping, composition, id)
lst.build(arr)

ans = [0]*Q

for i in range(Q):
  l, r, d = map(int, input().split())
  lst.range_apply(l - 1, r, d)
  v = lst.all_prod()
  ans[i] = v//po32

print(*ans, sep='\n')