package yukicoder_4596; import java.io.File; import java.io.FileInputStream; import java.io.FileNotFoundException; import java.io.IOException; import java.io.InputStream; import java.util.BitSet; import java.util.NoSuchElementException; public class Main { public static void main(String[] args) { new Main(); } public Main() { InputChecker ic = new InputChecker(System.in); java.io.PrintWriter out = new java.io.PrintWriter(System.out); solve(ic, out); out.flush(); ic.checkEOF(); } public void solve(InputChecker ic, java.io.PrintWriter out) { int W = ic.nextInt(1, 600); ic.nextChar(' '); int H = ic.nextInt(1, 600); ic.nextChar(' '); int X = ic.nextInt(0, 81); ic.readNewLine(); final int MOD = 998244353; final int N = 10, Nw = W % 3 == 2 ? N : 1, Nh = H % 3 == 2 ? N : 1, Na = N - 1; final int Cw = (W + 2) / 3, Ch = (H + 2) / 3; int ans = 0; if (W == 1) { if (H == 1) { ans = Na >= X ? 1 : 0; } else { if (H % 3 == 2) { for (int i = 0;i < N;++ i) { if (isRange(i, X - Na, X)) ++ ans; } } else { ans = Na >= X ? 1 : 0; } } } else { if (H == 1) { if (W % 3 == 2) { for (int i = 0;i < N;++ i) { if (isRange(i, X - Na, X)) ++ ans; } } else { ans = Na >= X ? 1 : 0; } } else { for (int a = 0;a < Math.min(Nw, Nh);++ a) { // M_{1,1} for (int l1 = 0, r1 = 0;r1 < Nw;++ l1) { // M_{1, 2w} if (l1 > r1) { l1 = 0; ++ r1; if (r1 >= Nw) break; } int comb1 = comb(l1, r1, Cw, MOD); for (int l2 = 0,r2 = 0;r2 < Nw;++ l2) { // M_{1, 2w + 1} if (l2 > r2) { if (W <= 2) break; // 実は存在しないため l2 = 0; ++ r2; if (r2 >= Nw) break; } int comb2 = comb(l2, r2, Cw - 1, MOD); for (int l3 = 0, r3 = 0;r3 < Nh;++ l3) { // M_{2h, 1} if (l3 > r3) { l3 = 0; ++ r3; if (r3 >= Nh) break; } int comb3 = comb(l3, r3, Ch, MOD); cont: for (int l4 = 0, r4 = 0;r4 < Nh;++ l4) { // M_{2h + 1, 1} if (l4 > r4) { if (H <= 2) break; // 実は存在しないため l4 = 0; ++ r4; if (r4 >= Nh) break; } for (int x = l1;W >= 2 && x <= r1;++ x) { for (int y = l3;H >= 2 && y <= r3;++ y) { // X - N <= M_{1, 1} + M_{1, 2w} + M_{2h, 1} <= X if (!isRange(a + x + y, X - Na, X)) continue cont; } for (int y = l4;H >= 3 && y <= r4;++ y) { // -N <= M_{1, 1} + M_{1, 2w} - M_{2h + 1, 1} <= 0 if (!isRange(a + x - y, -Na, 0)) continue cont; } } for (int x = l2;W >= 3 && x <= r2;++ x) { for (int y = l3;H >= 2 && y <= r3;++ y) { // -N <= M_{1, 1} + M_{2h, 1} - M_{1, 2w + 1} <= 0 if (!isRange(a - x + y, -Na, 0)) continue cont; } for (int y = l4;H >= 3 && y <= r4;++ y) { // 0 <= M_{1, 1} - M_{1, 2w + 1} - M_{2h + 1, 1} <= N if (!isRange(a - x - y, 0, Na)) continue cont; } } int comb4 = comb(l4, r4, Ch - 1, MOD); ans += (int)((long) comb1 * comb2 % MOD * comb3 % MOD * comb4 % MOD); ans %= MOD; } } } } } } } out.println(ans); } public static boolean isRange(int n, int l, int r) { return l <= n && n <= r; } public static int comb(int l, int r, int N, int mod) { final int d = r - l; if (d <= 0) return Math.max(0, d + 1); long ans = (long)pow(d + 1, N, mod) - (pow(d, N, mod) * 2) + pow(d - 1, N, mod); ans %= mod; if (ans < 0) ans += mod; return (int)ans; } public static int pow(int a, int b, int mod) { if (b < 0) b = b % (mod - 1) + mod - 1; long ans = 1; for (long mul = a;b > 0;b >>= 1, mul = mul * mul % mod) if ((b & 1) != 0) ans = ans * mul % mod; return (int)ans; } public static class CharSet { private final BitSet set = new BitSet(256); public void add(char... c) { for (char i : c) set.set(i); } public void add(CharSet... s) { for (CharSet i : s) set.or(i.set); } public boolean contains(char... c) { for (char i : c) if (!set.get(i)) return false; return true; } public boolean contains(String s) { return contains(s.toCharArray()); } private static final class Chars extends CharSet { public Chars(char... c) { super.add(c); } public Chars(CharSet... s) { super.add(s); } @Override public void add(char... c) { throw new UnsupportedOperationException(); } @Override public void add(CharSet... s) { throw new UnsupportedOperationException(); } } public static final CharSet NUMBER = new Chars('0','1','2','3','4','5','6','7','8','9'); public static final CharSet LOWER = new Chars('a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'); public static final CharSet UPPER = new Chars('A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z'); public static final CharSet ALPHABET = new Chars(LOWER, UPPER); } public static class InputChecker { private InputStream in; private final byte[] buffer = new byte[1024]; private final byte[] undo = new byte[1024]; private int undoSize = 0; private int read = 0; private int length = 0; public InputChecker(InputStream in) { this.in = in; } public final void setInputStream(InputStream in) { this.in = in; } public final void setInputStream(File in) { try { this.in = new FileInputStream(in); } catch (FileNotFoundException e) { e.printStackTrace(); } } private boolean hasNextByte() { if (undoSize > 0) return true; if (read < length) return true; read = 0; try { length = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } return length > 0; } private byte readByte() { if (hasNextByte()) return undoSize > 0 ? undo[--undoSize] : buffer[read++]; throw new NoSuchElementException(); } private void undo(byte b) { undo[undoSize ++] = b; } private void undo(char c) { if ((c & 0xFF80) == 0) { undo((byte)c); return; } undo((byte)(c & 0x3F | 0x80)); if ((c & 0xF800) == 0) { undo((byte)(c >> 6 & 0x1F | 0xC0)); } else { undo((byte)(c >> 6 & 0x3F | 0x80)); undo((byte)(c >> 12 | 0xE0)); } } public final boolean hasNext() { return hasNextByte(); } public final char nextChar() { byte b = readByte(); if ((b & 0x80) == 0) return (char)b; if ((b & 0x20) == 0) return (char)((b & 0x1F) << 6 | (readByte() & 0x3F)); return (char)((b & 0xF) << 12 | (readByte() & 0x3F) << 6 | (readByte() & 0x3F)); } public final char nextChar(char estimate) { char c = nextChar(); if (estimate == c) return estimate; undo(c); throw new AssertionError(); } public final char nextChar(CharSet estimate) { char c = nextChar(); if (estimate.contains(c)) return c; undo(c); throw new AssertionError(); } public final void readNewLine() { char c = nextChar(); if (c == '\r') { c = nextChar(); if (c != '\n') undo(c); return; } else if (c == '\n') return; undo(c); throw new AssertionError(); } public final void checkEOF() { if (hasNextByte()) throw new AssertionError(); } public final String next(CharSet contains) { StringBuilder sb = new StringBuilder(); try { do { char c = nextChar(); if (!contains.contains(c)) { undo(c); return sb.toString(); } sb.append(c); } while(true); } catch (NoSuchElementException e) { if (sb.length() <= 0) throw new AssertionError(); return sb.toString(); } } public final int nextInt() { byte b = readByte(); int n = 0; if (b == '-') { if (!isNumber(b = readByte())) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), '0' - b); while(isNumber(b = readByte())); undo(b); } catch (NoSuchElementException e) { } return n; } if (!isNumber(b)) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), b - '0'); while(isNumber(b = readByte())); undo(b); } catch (NoSuchElementException e) { } return n; } public final int nextInt(int min, int max) { int n = nextInt(); if (min <= n && n <= max) return n; throw new NumberFormatException(); } private static boolean isNumber(byte c) { return '0' <= c && c <= '9'; } public final long nextLong() { byte b = readByte(); long n = 0; if (b == '-') { if (!isNumber(b = readByte())) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), '0' - b); while(isNumber(b = readByte())); undo(b); } catch (NoSuchElementException e) { } return n; } if (!isNumber(b)) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), b - '0'); while(isNumber(b = readByte())); undo(b); } catch (NoSuchElementException e) { } return n; } public final long nextLong(long min, long max) { long n = nextLong(); if (min <= n && n <= max) return n; throw new NumberFormatException(); } public final double nextDouble() { StringBuilder sb = new StringBuilder(); byte b = readByte(); if (b == '-') { sb.append(b); b = readByte(); } if (b == '0') { sb.append(b); b = readByte(); } else { while(isNumber(b)) { sb.append(b); b = readByte(); } } if (b == '.') { sb.append(b); b = readByte(); while(isNumber(b)) { sb.append(b); b = readByte(); } } if (b == 'e' || b == 'E') { sb.append(b); b = readByte(); if (b == '-' || b == '+') { sb.append(b); b = readByte(); } while(isNumber(b)) { sb.append(b); b = readByte(); } } undo(b); return Double.parseDouble(sb.toString()); } } }