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:
N, Q, *LRD = [int(_) for _ in open(0).read().split()]
L, R, D = LRD[::3], LRD[1::3], LRD[2::3]
mod = 998244353


class LazySegmentTree:

    __slots__ = ["n", "data", "lazy", "me", "oe", "fmm", "fmo", "foo"]

    def __init__(self, monoid_data, monoid_identity, operator_identity,
                 func_monoid_monoid, func_monoid_operator,
                 func_operator_operator):
        self.me = monoid_identity
        self.oe = operator_identity
        self.fmm = func_monoid_monoid
        self.fmo = func_monoid_operator
        self.foo = func_operator_operator

        self.n = len(monoid_data)
        self.data = monoid_data * 2
        for i in range(self.n - 1, 0, -1):
            self.data[i] = self.fmm(self.data[2 * i], self.data[2 * i + 1])
        self.lazy = [self.oe] * (self.n * 2)

    def replace(self, index, value):
        index += self.n

        # propagation
        for shift in range(index.bit_length() - 1, 0, -1):
            i = index >> shift
            self.lazy[2 * i] = self.foo(self.lazy[2 * i], self.lazy[i])
            self.lazy[2 * i + 1] = self.foo(self.lazy[2 * i + 1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # update
        self.data[index] = value
        self.lazy[index] = self.oe

        # recalculation
        i = index
        while i > 1:
            i //= 2
            self.data[i] = self.fmm(
                self.fmo(self.data[2 * i], self.lazy[2 * i]),
                self.fmo(self.data[2 * i + 1], self.lazy[2 * i + 1]))
            self.lazy[i] = self.oe

    def effect(self, l, r, operator):
        l += self.n
        r += self.n

        # preparing indices
        indices = []
        l0 = (l // (l & -l)) // 2
        r0 = (r // (r & -r) - 1) // 2
        while r0 > l0:
            indices.append(r0)
            r0 //= 2
        while l0 > r0:
            indices.append(l0)
            l0 //= 2
        while l0 and l0 != r0:
            indices.append(r0)
            r0 //= 2
            if l0 == r0:
                break
            indices.append(l0)
            l0 //= 2
        while r0:
            indices.append(r0)
            r0 //= 2

        # propagation
        for i in reversed(indices):
            self.lazy[2 * i] = self.foo(self.lazy[2 * i], self.lazy[i])
            self.lazy[2 * i + 1] = self.foo(self.lazy[2 * i + 1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # effect
        while l < r:
            if l % 2:
                self.lazy[l] = self.foo(self.lazy[l], operator)
                l += 1
            if r % 2:
                r -= 1
                self.lazy[r] = self.foo(self.lazy[r], operator)
            l //= 2
            r //= 2

        # recalculation
        for i in indices:
            self.data[i] = self.fmm(
                self.fmo(self.data[2 * i], self.lazy[2 * i]),
                self.fmo(self.data[2 * i + 1], self.lazy[2 * i + 1]))
            self.lazy[i] = self.oe

    def folded(self, l, r):
        l += self.n
        r += self.n

        # preparing indices
        indices = []
        l0 = (l // (l & -l)) // 2
        r0 = (r // (r & -r) - 1) // 2
        while r0 > l0:
            indices.append(r0)
            r0 //= 2
        while l0 > r0:
            indices.append(l0)
            l0 //= 2
        while l0 and l0 != r0:
            indices.append(r0)
            r0 //= 2
            if l0 == r0:
                break
            indices.append(l0)
            l0 //= 2
        while r0:
            indices.append(r0)
            r0 //= 2

        # propagation
        for i in reversed(indices):
            self.lazy[2 * i] = self.foo(self.lazy[2 * i], self.lazy[i])
            self.lazy[2 * i + 1] = self.foo(self.lazy[2 * i + 1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # fold
        left_folded = self.me
        right_folded = self.me
        while l < r:
            if l % 2:
                left_folded = self.fmm(left_folded,
                                       self.fmo(self.data[l], self.lazy[l]))
                l += 1
            if r % 2:
                r -= 1
                right_folded = self.fmm(self.fmo(self.data[r], self.lazy[r]),
                                        right_folded)
            l //= 2
            r //= 2
        return self.fmm(left_folded, right_folded)


#RSQ and RUQ
array = [(pow(10, i, mod), pow(10, i, mod)) for i in range(N)][::-1]
f = lambda a, b: ((a[0] + b[0]) % mod, (a[1] + b[1]) % mod)
g = lambda a, b: (b * a[1] % mod, a[1]) if b else a
h = lambda a, b: b if b else a
ti = (0, 0)
ei = 0

lst = LazySegmentTree(array, ti, ei, f, g, h)
ans = []
for l, r, d in zip(L, R, D):
    lst.effect(l - 1, r, d)
    ans += [lst.folded(0, N)[0]]
print('\n'.join(map(str, ans)))