## https://yukicoder.me/problems/no/669 MOD = 998244353 from collections import deque class CombinationCalculator: """ modを考慮したPermutation, Combinationを計算するためのクラス """ def __init__(self, size, mod): self.mod = mod self.factorial = [0] * (size + 1) self.factorial[0] = 1 for i in range(1, size + 1): self.factorial[i] = (i * self.factorial[i - 1]) % self.mod self.inv_factorial = [0] * (size + 1) self.inv_factorial[size] = pow(self.factorial[size], self.mod - 2, self.mod) for i in reversed(range(size)): self.inv_factorial[i] = ((i + 1) * self.inv_factorial[i + 1]) % self.mod def calc_combination(self, n, r): if n < 0 or n < r or r < 0: return 0 if r == 0 or n == r: return 1 ans = self.inv_factorial[n - r] * self.inv_factorial[r] ans %= self.mod ans *= self.factorial[n] ans %= self.mod return ans def calc_permutation(self, n, r): if n < 0 or n < r: return 0 ans = self.inv_factorial[n - r] ans *= self.factorial[n] ans %= self.mod return ans class BinaryIndexTree: """ フェニック木(BinaryIndexTree)の基本的な機能を実装したクラス """ def __init__(self, size): self.size = size self.array = [0] * (size + 1) def add(self, x, a): index = x while index <= self.size: self.array[index] += a index += index & (-index) def sum(self, x): index = x ans = 0 while index > 0: ans += self.array[index] index -= index & (-index) return ans def least_upper_bound(self, value): if self.sum(self.size) < value: return -1 elif value <= 0: return 0 m = 1 while m < self.size: m *= 2 k = 0 k_sum = 0 while m > 0: k0 = k + m if k0 < self.size: if k_sum + self.array[k0] < value: k_sum += self.array[k0] k += m m //= 2 if k < self.size: return k + 1 else: return -1 def main(): N, M = map(int ,input().split()) pk = [] for _ in range(M): p, k = map(int, input().split()) pk.append((p , k)) free_n = N - M combi = CombinationCalculator(N, MOD) # 固定しているもの同士 pk.sort(key=lambda x : x[1]) bit = BinaryIndexTree(N + 1) ans = 0 for p, _ in pk: ans += bit.sum(bit.size) - bit.sum(p) bit.add(p, 1) ans1 = (ans * combi.factorial[free_n]) % MOD # 自由に動くもの同士 x = (free_n * (free_n - 1)) % MOD x *= pow(4, MOD - 2, MOD) x %= MOD ans2 = (x * combi.factorial[free_n]) % MOD # 固定しているもの x 自由に動くもの k_map = {(k - 1): p for p, k in pk} p_right = {} p_left = {} queue = deque() for i in range(N): if i in k_map: queue.append(k_map[i]) else: while len(queue) > 0: p = queue.popleft() p_right[p] = i for i in reversed(range(N)): if i in k_map: queue.append(k_map[i]) else: while len(queue) > 0: p = queue.popleft() p_left[p] = i k_set = set() for k in range(N): if k not in k_map: k_set.add(k) k_list = list(k_set) k_list.sort() c_k_map = {} for i, p in enumerate(k_list): c_k_map[p] = i prob_left = 0 for p, k in pk: if p in p_left: prob_left += c_k_map[p_left[p]] + 1 p_map = {p:k for p, k in pk} prob_right =0 ans3 = 0 for p in reversed(range(1, N + 1)): if p in p_map: if p in p_left: prob_left -= c_k_map[p_left[p]] + 1 if p in p_right: prob_right += free_n - c_k_map[p_right[p]] else: a = (prob_left + prob_right) % MOD a *= pow(free_n, MOD - 2, MOD) a %= MOD a *= combi.factorial[free_n] a %= MOD ans3 += a ans3 %= MOD answer = (ans1 + ans2) % MOD answer += ans3 answer %= MOD print(answer) if __name__ == "__main__": main()