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.d = [e] * (2 * self.size)
        self.lz = [id] * (self.size)

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

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

    def push(self, k):
        self.all_apply(2 * k, self.lz[k])
        self.all_apply(2 * k + 1, self.lz[k])
        self.lz[k] = self.id

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

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

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

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

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

import sys
input = sys.stdin.buffer.readline

INF = 10**18
MOD = 998244353

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

def op(x, y):
    xv, xr = x >> 32, x % (1 << 32)
    yv, yr = y >> 32, y % (1 << 32)
    return ((xv + yv) % MOD << 32) + (xr + yr) % MOD

def mapping(p, x):
    xv, xr = x >> 32, x % (1 << 32)
    if p != INF:
        return ((p * xr % MOD) << 32) + xr
    else:
        return x

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

def build_exp(n, b):
    res = [0] * (n + 1)
    res[0] = 1
    for i in range(n):
        res[i + 1] = res[i] * b % MOD
    return res

exp = build_exp(N - 1, 10)

arr = [(e << 32) + e for e in exp[::-1]]

e = 0
id = INF

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

res = list()

for _ in range(Q):
    l, r, d = map(int, input().split())
    lst.range_apply(l - 1, r, d)
    v = lst.all_prod()
    res.append(v >> 32)


print('\n'.join(map(str, res)))