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:
# でつoO(YOU PLAY WITH THE CARDS YOU'RE DEALT..)
import typing
import sys
MOD = 998244353
def main(N, Q, LRD):
    inv9 = pow(9, MOD - 2, MOD)
    tree = LazySegTree(
        op=lambda x, y: (((x[0] * y[1]) % MOD + y[0]) % MOD, (x[1] * y[1]) % MOD),
        e=(0, 1),
        mapping=lambda f, s: s if f == 0 else (((s[1] - 1) * inv9 * f) % MOD, s[1]),
        composition=lambda f, g: g if f == 0 else f,
        id_=0,
        v=[(1, 10)] * N)

    for l, r, d in LRD:
        l -= 1
        tree.apply(l, r, d)
        print(tree.all_prod()[0])

class LazySegTree:
    def __init__(
            self,
            op: typing.Callable[[typing.Any, typing.Any], typing.Any],
            e: typing.Any,
            mapping: typing.Callable[[typing.Any, typing.Any], typing.Any],
            composition: typing.Callable[[typing.Any, typing.Any], typing.Any],
            id_: typing.Any,
            v: typing.Union[int, typing.List[typing.Any]]) -> None:
        self._op = op
        self._e = e
        self._mapping = mapping
        self._composition = composition
        self._id = id_

        if isinstance(v, int):
            v = [e] * v

        self._n = len(v)
        self._log = self._n.bit_length()
        self._size = 1 << self._log
        self._d = [e] * (2 * self._size)
        self._lz = [self._id] * self._size
        for i in range(self._n):
            self._d[self._size + i] = v[i]
        for i in range(self._size - 1, 0, -1):
            self._update(i)

    def set(self, p: int, x: typing.Any) -> None:
        assert 0 <= p < self._n

        p += self._size
        for i in range(self._log, 0, -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: int) -> typing.Any:
        assert 0 <= p < self._n

        p += self._size
        for i in range(self._log, 0, -1):
            self._push(p >> i)
        return self._d[p]

    def prod(self, left: int, right: int) -> typing.Any:
        assert 0 <= left <= right <= self._n

        if left == right:
            return self._e

        left += self._size
        right += self._size

        for i in range(self._log, 0, -1):
            if ((left >> i) << i) != left:
                self._push(left >> i)
            if ((right >> i) << i) != right:
                self._push(right >> i)

        sml = self._e
        smr = self._e
        while left < right:
            if left & 1:
                sml = self._op(sml, self._d[left])
                left += 1
            if right & 1:
                right -= 1
                smr = self._op(self._d[right], smr)
            left >>= 1
            right >>= 1

        return self._op(sml, smr)

    def all_prod(self) -> typing.Any:
        return self._d[1]

    def apply(self, left: int, right: typing.Optional[int] = None,
              f: typing.Optional[typing.Any] = None):
        assert f is not None

        if right is None:
            p = left
            assert 0 <= left < self._n

            p += self._size
            for i in range(self._log, 0, -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)
        else:
            assert 0 <= left <= right <= self._n
            if left == right:
                return

            left += self._size
            right += self._size

            for i in range(self._log, 0, -1):
                if ((left >> i) << i) != left:
                    self._push(left >> i)
                if ((right >> i) << i) != right:
                    self._push((right - 1) >> i)

            l2 = left
            r2 = right
            while left < right:
                if left & 1:
                    self._all_apply(left, f)
                    left += 1
                if right & 1:
                    right -= 1
                    self._all_apply(right, f)
                left >>= 1
                right >>= 1
            left = l2
            right = r2

            for i in range(1, self._log + 1):
                if ((left >> i) << i) != left:
                    self._update(left >> i)
                if ((right >> i) << i) != right:
                    self._update((right - 1) >> i)

    def max_right(
            self, left: int, g: typing.Callable[[typing.Any], bool]) -> int:
        assert 0 <= left <= self._n
        assert g(self._e)

        if left == self._n:
            return self._n

        left += self._size
        for i in range(self._log, 0, -1):
            self._push(left >> i)

        sm = self._e
        first = True
        while first or (left & -left) != left:
            first = False
            while left % 2 == 0:
                left >>= 1
            if not g(self._op(sm, self._d[left])):
                while left < self._size:
                    self._push(left)
                    left *= 2
                    if g(self._op(sm, self._d[left])):
                        sm = self._op(sm, self._d[left])
                        left += 1
                return left - self._size
            sm = self._op(sm, self._d[left])
            left += 1

        return self._n

    def min_left(self, right: int, g: typing.Any) -> int:
        assert 0 <= right <= self._n
        assert g(self._e)

        if right == 0:
            return 0

        right += self._size
        for i in range(self._log, 0, -1):
            self._push((right - 1) >> i)

        sm = self._e
        first = True
        while first or (right & -right) != right:
            first = False
            right -= 1
            while right > 1 and right % 2:
                right >>= 1
            if not g(self._op(self._d[right], sm)):
                while right < self._size:
                    self._push(right)
                    right = 2 * right + 1
                    if g(self._op(self._d[right], sm)):
                        sm = self._op(self._d[right], sm)
                        right -= 1
                return right + 1 - self._size
            sm = self._op(self._d[right], sm)

        return 0

    def _update(self, k: int) -> None:
        self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])

    def _all_apply(self, k: int, f: typing.Any) -> None:
        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: int) -> None:
        self._all_apply(2 * k, self._lz[k])
        self._all_apply(2 * k + 1, self._lz[k])
        self._lz[k] = self._id

if __name__ == '__main__':
    input = sys.stdin.readline
    N, Q = map(int, input().split())
    LRD = [tuple(map(int, input().split())) for _ in range(Q)]
    main(N, Q, LRD)