#include const int Mod = 998244353; typedef struct HList { struct HList *next; int u, w; } hlist; #define HASH 5000011 const int H_Mod = HASH; int hash_func(int u, int w) { return (((long long)u << 30) + w) % H_Mod; } int hn = 0; hlist *hash[HASH] = {}, hd[200001]; int is_adjacent(int u, int w) { if (u > w) { u ^= w; w ^= u; u ^= w; } int h; hlist *hp; h = hash_func(u, w); for (hp = hash[h]; hp != NULL; hp = hp->next) if (hp->u == u && hp->w == w) return 1; return 0; } typedef struct Edge { struct Edge *next; int v; } edge; typedef struct { int key, id; } data; typedef struct { data obj[400001]; int size; } min_heap; void push(min_heap* h, data x) { int i = ++(h->size), j = i >> 1; data tmp; h->obj[i] = x; while (j > 0) { if (h->obj[i].key < h->obj[j].key) { tmp = h->obj[j]; h->obj[j] = h->obj[i]; h->obj[i] = tmp; i = j; j >>= 1; } else break; } } data pop(min_heap* h) { int i = 1, j = 2; data output = h->obj[1], tmp; h->obj[1] = h->obj[(h->size)--]; while (j <= h->size) { if (j < h->size && h->obj[j^1].key < h->obj[j].key) j ^= 1; if (h->obj[j].key < h->obj[i].key) { tmp = h->obj[j]; h->obj[j] = h->obj[i]; h->obj[i] = tmp; i = j; j <<= 1; } else break; } return output; } void count_triangles_sub(int n, int v[], long long *num_edge, long long *num_triangle) { int i, j, k; static int adj_mat[1001][1001] = {}; for (i = 1, *num_edge = 0; i <= n; i++) for (j = i + 1; j <= n; j++) if (is_adjacent(v[i], v[j]) != 0) { adj_mat[i][j] = 1; (*num_edge)++; } if (*num_edge == n * (n - 1) / 2) *num_triangle = n * (n - 1) * (n - 2) / 6; else if (*num_edge == n * (n - 1) / 2 - 1) *num_triangle = n * (n - 1) * (n - 2) / 6 - (n - 2); else { for (i = 1, *num_triangle = 0; i <= n; i++) for (j = i + 1; j <= n; j++) for (k = j + 1; k <= n; k++) *num_triangle += adj_mat[i][j] & adj_mat[i][k] & adj_mat[j][k]; } for (i = 1; i <= n; i++) for (j = i + 1; j <= n; j++) adj_mat[i][j] = 0; } int main() { int i, N, M, U[200001], V[200001]; scanf("%d %d", &N, &M); for (i = 1; i <= M; i++) { scanf("%d %d", &(U[i]), &(V[i])); if (U[i] > V[i]) { U[i] ^= V[i]; V[i] ^= U[i]; U[i] ^= V[i]; } } if (N <= 3) { printf("0 0\n"); return 0; } int h, u, w, ed[200001][2]; for (i = 1; i <= M; i++) { u = U[i]; w = V[i]; ed[i][0] = u; ed[i][1] = w; h = hash_func(u, w); hd[hn].u = u; hd[hn].w = w; hd[hn].next = hash[h]; hash[h] = &(hd[hn++]); } int deg[200001] = {}; edge *adj[200001] = {}, e[400001], *ep; for (i = 1; i <= M; i++) { u = ed[i][0]; w = ed[i][1]; e[i*2-1].v = w; e[i*2-1].next = adj[u]; adj[u] = &(e[i*2-1]); e[i*2].v = u; e[i*2].next = adj[w]; adj[w] = &(e[i*2]); deg[u]++; deg[w]++; } int r, flag[200001] = {}, q[200001], j, tail; long long ans, tmp; ans = (__int128)N * (N - 1) * (N - 2) * (N - 3) / 24 % Mod; ans += Mod - (long long)M * (N - 2) * (N - 3) / 2 % Mod; for (u = 1, tmp = (long long)M * (M - 1) / 2; u <= N; u++) { tmp -= (long long)deg[u] * (deg[u] - 1) / 2; ans += (long long)deg[u] * (deg[u] - 1) / 2 * (N - 3) % Mod; ans += Mod - (long long)deg[u] * (deg[u] - 1) * (deg[u] - 2) / 6 % Mod; } ans += tmp; for (i = 1; i <= M; i++) { u = ed[i][0]; w = ed[i][1]; ans += Mod - (long long)(deg[u] - 1) * (deg[w] - 1) % Mod; } for (u = 1; u <= N; u++) { for (ep = adj[u], tail = 0; ep != NULL; ep = ep->next) { w = ep->v; flag[w] = 1; q[++tail] = w; } if (tail >= 3) { if (tail <= 500) { for (i = 1, tmp = 0; i <= tail; i++) for (j = i + 1; j <= tail; j++) tmp += is_adjacent(q[i], q[j]); } else { for (i = 1; i <= M; i++) if (flag[ed[i][0]] != 0 && flag[ed[i][1]] != 0) tmp++; } ans += tmp * (tail - 2) % Mod; for (i = 1; i <= tail; i++) flag[q[i]] = 0; } } long long num_triangle = 0, tmp_num_edge, tmp_num_triangle; min_heap he; data d; he.size = 0; for (u = 1; u <= N; u++) { d.key = deg[u]; d.id = u; push(&he, d); } while (he.size > 0) { d = pop(&he); u = d.id; if (flag[u] != 0) continue; flag[u] = 1; for (ep = adj[u], tail = 0; ep != NULL; ep = ep->next) { w = ep->v; if (flag[w] == 0) { q[++tail] = w; deg[w]--; d.key = deg[w]; d.id = w; push(&he, d); } } for (i = 1; i <= tail; i++) for (j = i + 1; j <= tail; j++) num_triangle += is_adjacent(q[i], q[j]); if (tail >= 3) { count_triangles_sub(tail, q, &tmp_num_edge, &tmp_num_triangle); // ans += tmp_num_edge * (tail - 2) % Mod; ans += Mod - tmp_num_triangle * 2 % Mod; } } ans += num_triangle * 3; ans += Mod - num_triangle * (N - 3) % Mod; printf("%d %lld\n", Mod - 1, ans % Mod); fflush(stdout); return 0; }