using System; using System.Collections.Generic; using System.Linq; using System.IO; using System.Threading; using System.Text; using System.Text.RegularExpressions; using System.Diagnostics; using static util; using P = pair; class Program { static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; var solver = new Solver(sw); // var t = new Thread(solver.solve, 1 << 28); // 256 MB // t.Start(); // t.Join(); solver.solve(); sw.Flush(); } } class Solver { StreamWriter sw; Scan sc; void Prt(string a) => sw.WriteLine(a); void Prt(IEnumerable a) => Prt(string.Join(" ", a)); void Prt(params object[] a) => Prt(string.Join(" ", a)); public Solver(StreamWriter sw) { this.sw = sw; this.sc = new Scan(); } public void solve() { int w, h, n; sc.Multi(out w, out h, out n); var dp = new long[1 << h][][]; for (int i = 0; i < (1 << h); i++) { dp[i] = new long[5][]; for (int j = 0; j < 5; j++) { dp[i][j] = new long[n + 1]; } } memo = new P[1 << h][][]; for (int i = 0; i < (1 << h); i++) { memo[i] = new P[1 << h][]; for (int j = 0; j < (1 << h); j++) { memo[i][j] = new P[5]; } } long ans = 0; cnt = new int[1 << h]; for (int i = 1; i < (1 << h); i++) { int c = 0; for (int j = 0; j < h; j++) { if (((i >> j) & 1) == 1 && (j == 0 || ((i >> (j - 1)) & 1) == 0)) { ++c; } } cnt[i] = c; if (c * 4 <= n) { if (c == 1) { ++dp[i][0][c * 4]; } else if (c == 2) { ++dp[i][1][c * 4]; } else { ++dp[i][4][c * 4]; } } ans += dp[i][0][n] * w; } for (int t = w - 1; t > 0 ; t--) { var nex = new long[1 << h][][]; for (int i = 0; i < (1 << h); i++) { nex[i] = new long[5][]; for (int j = 0; j < 5; j++) { nex[i][j] = new long[n + 1]; } } for (int i = 1; i < (1 << h); i++) { for (int j = 0; j < 5; j++) { for (int k = 0; k < n + 1; k++) { if (dp[i][j][k] == 0) continue; // Assert(k % 2 == 0); for (int l = 1; l < (1 << h); l++) { var nx = next(h, i, l, j); // DBG(nx); if (nx.v1 == -1) continue; if (k + nx.v2 <= n) { nex[l][nx.v1][k + nx.v2] = (nex[l][nx.v1][k + nx.v2] + dp[i][j][k]) % M; } } } } } dp = nex; for (int i = 1; i < (1 << h); i++) { ans = (ans + dp[i][0][n] * t) % M; } } Prt(ans); } int[] cnt; P[][][] memo; int calc_c(int h, int b1, int b2) { int res = 0; { int c = 0; c += (b1 >> 0) & 1; c += (b2 >> 0) & 1; if (c % 2 == 1) ++res; } { int c = 0; c += (b1 >> (h - 1)) & 1; c += (b2 >> (h - 1)) & 1; if (c % 2 == 1) ++res; } for (int i = 0; i < h - 1; i++) { int c = 0; c += (b1 >> i) & 1; c += (b1 >> (i + 1)) & 1; c += (b2 >> i) & 1; c += (b2 >> (i + 1)) & 1; if (c % 2 == 1) ++res; } return res; } int calc_diff(int h, int b1, int b2) { return -calc_c(h, b1, 0) + calc_c(h, b1, b2) + calc_c(h, b2, 0); } bool check1(int h, int b1, int b2) { for (int i = 0; i < h - 1; i++) { bool b11 = ((b1 >> i) & 1) == 1; bool b12 = ((b1 >> (i + 1)) & 1) == 1; bool b21 = ((b2 >> i) & 1) == 1; bool b22 = ((b2 >> (i + 1)) & 1) == 1; if (b11 && b22 && !b12 && !b21) { return false; } if (!b11 && !b22 && b12 && b21) { return false; } } return true; } int next_con(int h, int b1, int b2, int con) { var uf = new UnionFind(h * 2); var b = new bool[2][]; b[0] = new bool[h]; b[1] = new bool[h]; var l1 = new List(); for (int j = 0; j < h; j++) { if (((b1 >> j) & 1) == 1 && (j == 0 || ((b1 >> (j - 1)) & 1) == 0)) { l1.Add(j); } } for (int i = 0; i < h; i++) { b[0][i] = ((b1 >> i) & 1) == 1; b[1][i] = ((b2 >> i) & 1) == 1; } for (int i = 0; i < h; i++) { if (b[0][i] && b[1][i]) { uf.unite(i, h + i); } for (int j = 0; j < 2; j++) { if (i + 1 < h && b[j][i] && b[j][i + 1]) { uf.unite(j * h + i, j * h + i + 1); } } } if (cnt[b1] == 2 && con == 0) { if (!uf.unite(l1[0], l1[1])) { return -1; } } if (cnt[b1] == 3) { if (con == 0) { if (!uf.unite(l1[0], l1[1])) { return -1; } if (!uf.unite(l1[0], l1[2])) { return -1; } } else if (con == 1) { if (!uf.unite(l1[0], l1[1])) { return -1; } } else if (con == 2) { if (!uf.unite(l1[0], l1[2])) { return -1; } } else if (con == 3) { if (!uf.unite(l1[1], l1[2])) { return -1; } } } foreach (var item in l1) { bool cc = false; for (int i = 0; i < h; i++) { cc |= uf.same(item, h + i); } if (!cc) { return -1; } } var l2 = new List(); for (int j = 0; j < h; j++) { if (((b2 >> j) & 1) == 1 && (j == 0 || ((b2 >> (j - 1)) & 1) == 0)) { l2.Add(j); } } if (cnt[b2] == 1) { return 0; } else if (cnt[b2] == 2) { if (uf.same(h + l2[0], h + l2[1])) { return 0; } else { return 1; } } else { if (uf.same(h + l2[0], h + l2[1]) && uf.same(h + l2[0], h + l2[2])) { return 0; } else if (uf.same(h + l2[0], h + l2[1])) { return 1; } else if (uf.same(h + l2[0], h + l2[2])) { return 2; } else if (uf.same(h + l2[1], h + l2[2])) { return 3; } else { return 4; } } } P next(int h, int b1, int b2, int con) { if (memo[b1][b2][con] != null) { return memo[b1][b2][con]; } if (!check1(h, b1, b2)) { return new P(-1, -1); } int nex_con = next_con(h, b1, b2, con); if (nex_con == -1) { return new P(-1, -1); } int diff = calc_diff(h, b1, b2); return new P(nex_con, diff); } } class pair : IComparable> { public T v1; public U v2; public pair() : this(default(T), default(U)) {} public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; } public int CompareTo(pair a) { int c = Comparer.Default.Compare(v1, a.v1); return c != 0 ? c : Comparer.Default.Compare(v2, a.v2); } public override string ToString() => $"{v1} {v2}"; public void Deconstruct(out T a, out U b) { a = v1; b = v2; } } static class util { // public static readonly int M = 1000000007; public static readonly int M = 998244353; public static readonly long LM = 1L << 60; public static readonly double eps = 1e-11; public static void DBG(string a) => Console.Error.WriteLine(a); public static void DBG(IEnumerable a) => DBG(string.Join(" ", a)); public static void DBG(params object[] a) => DBG(string.Join(" ", a)); public static void Assert(params bool[] conds) { if (conds.Any(x => !x)) throw new Exception(); } public static pair make_pair(T v1, U v2) => new pair(v1, v2); public static int CompareList(IList a, IList b) where T : IComparable { for (int i = 0; i < a.Count && i < b.Count; i++) if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]); return a.Count.CompareTo(b.Count); } public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w; public static readonly int[] dd = { 0, 1, 0, -1 }; // static readonly string dstring = "RDLU"; public static IEnumerable

adjacents(int i, int j) { for (int k = 0; k < 4; k++) yield return new P(i + dd[k], j + dd[k ^ 1]); } public static IEnumerable

adjacents(int i, int j, int h, int w) { for (int k = 0; k < 4; k++) if (inside(i + dd[k], j + dd[k ^ 1], h, w)) yield return new P(i + dd[k], j + dd[k ^ 1]); } public static IEnumerable

adjacents(this P p) => adjacents(p.v1, p.v2); public static IEnumerable

adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w); public static IEnumerable all_subset(this int p) { for (int i = 0; ; i = i - p & p) { yield return i; if (i == p) break; } } public static Dictionary compress(this IEnumerable a) => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i); public static Dictionary compress(params IEnumerable[] a) => compress(a.SelectMany(x => x)); public static T[] inv(this Dictionary dic) { var res = new T[dic.Count]; foreach (var item in dic) res[item.Value] = item.Key; return res; } public static void swap(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; } public static void swap(this IList a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; } public static T[] copy(this IList a) { var ret = new T[a.Count]; for (int i = 0; i < a.Count; i++) ret[i] = a[i]; return ret; } } class Scan { StreamReader sr; public Scan() { sr = new StreamReader(Console.OpenStandardInput()); } public Scan(string path) { sr = new StreamReader(path); } public int Int => int.Parse(Str); public long Long => long.Parse(Str); public double Double => double.Parse(Str); public string Str => ReadLine.Trim(); public string ReadLine => sr.ReadLine(); public pair Pair() { T a; U b; Multi(out a, out b); return new pair(a, b); } public P P => Pair(); public int[] IntArr => StrArr.Select(int.Parse).ToArray(); public long[] LongArr => StrArr.Select(long.Parse).ToArray(); public double[] DoubleArr => StrArr.Select(double.Parse).ToArray(); public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries); bool eq() => typeof(T).Equals(typeof(U)); T ct(U a) => (T)Convert.ChangeType(a, typeof(T)); T cv(string s) => eq() ? ct(int.Parse(s)) : eq() ? ct(long.Parse(s)) : eq() ? ct(double.Parse(s)) : eq() ? ct(s[0]) : ct(s); public void Multi(out T a) => a = cv(Str); public void Multi(out T a, out U b) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); } public void Multi(out T a, out U b, out V c) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); } public void Multi(out T a, out U b, out V c, out W d) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); } public void Multi(out T a, out U b, out V c, out W d, out X e) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); } public void Multi(out T a, out U b, out V c, out W d, out X e, out Y f) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); f = cv(ar[5]); } } class UnionFind { int num; int[] par, sz, rank; public UnionFind(int n) { num = n; par = new int[n]; sz = new int[n]; rank = new int[n]; for (int i = 0; i < n; ++i) { par[i] = i; sz[i] = 1; rank[i] = 0; } } int find(int x) => par[x] == x ? x : (par[x] = find(par[x])); public bool same(int x, int y) => find(x) == find(y); public int unionsize(int x) => sz[find(x)]; public int unioncount => num; public bool unite(int x, int y) { x = find(x); y = find(y); if (x == y) return false; --num; if (rank[x] < rank[y]) { par[x] = y; sz[y] += sz[x]; } else { par[y] = x; sz[x] += sz[y]; if (rank[x] == rank[y]) ++rank[x]; } return true; } public bool ispar(int x) => x == find(x); public int getpar(int x) => find(x); }