package contest210924; import java.io.*; import java.util.*; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; public class F3 { InputStream is; FastWriter out; String INPUT = ""; public static class CombinationParser { final int mod; final int[][] fif; public CombinationParser(int mod, int n){ this.mod = mod; this.fif = enumFIF(n, mod); } char[] s; int pos, len; Map values; public long parsei(String S, Map values){ this.values = new HashMap<>(); for(String key : values.keySet()){ this.values.put(key, values.get(key).longValue()); } return parse(S, this.values); } public long parse(String S, Map values){ s = S.replace(" ", "").toCharArray(); pos = 0; len = s.length; this.values = values; long res = exprpm(); if(pos != len)throw new AssertionError("pos != len: " + pos + " " + len); return res; } // +- long exprpm() { long v = exprmd(); while(pos < len){ if(s[pos] == '+'){ pos++; v += exprmd(); }else if(s[pos] == '-'){ pos++; v -= exprmd(); }else{ break; } } v %= mod; if(v < 0)v += mod; return v; } // */ long exprmd() { long v = expre(); while(pos < len){ if(s[pos] == '*'){ if(pos+1 < len && s[pos+1] == '*'){ break; } pos++; v = v * expre() % mod; }else if(s[pos] == '/'){ pos++; long res = expre(); if(res == 0)throw new AssertionError("divide by zero: " + pos); v = v * invl(res, mod) % mod; }else if(s[pos] == '+' || s[pos] == '-' || s[pos] == ')' || s[pos] == ',') { break; }else{ // 乗算とみなす v = v * expre() % mod; break; } } return v; } long expre() { long v = expr(); if(pos >= len)return v; if(s[pos] == '*' && pos+1 < len && s[pos+1] == '*'){ pos+=2; v = pow(v, expr(), mod); }else if(s[pos] == '^') { pos++; v = pow(v, expr(), mod); } return v; } long expr() { if(s[pos] == '('){ pos++; long res = exprpm(); expect(')'); pos++; if(pos < len && s[pos] == '!'){ res = F((int)res); pos++; } return res; }else if(s[pos] == '-'){ // 単項minus pos++; long res = item(); res = -res; if(res < 0)res += mod; return res; }else{ return item(); } } void expect(char c) { if(s[pos] != c)throw new AssertionError("expect '" + c + "' @" + pos); } long item() { if(s[pos] == 'C' && pos+1 < len && s[pos+1] == '('){ pos++; pos++; long n = exprpm(); expect(','); pos++; long r = exprpm(); expect(')'); pos++; return C((int)n, (int)r, mod, fif); }else if('0' <= s[pos] && s[pos] <= '9'){ // 即値 long val = 0; while(pos < len && '0' <= s[pos] && s[pos] <= '9'){ val = (val * 10 + s[pos]-'0') % mod; pos++; } long res = val; if(pos < len && s[pos] == '!'){ res = F((int)res); pos++; } return res; }else{ // 変数 StringBuilder v = new StringBuilder(); while(pos < len && ( 'a' <= s[pos] && s[pos] <= 'z' || 'A' <= s[pos] && s[pos] <= 'Z' || '0' <= s[pos] && s[pos] <= '9' )){ v.append(s[pos]); pos++; } if (!values.containsKey(v.toString())) { throw new AssertionError("undefined variable: " + v + " @" + pos); } long res = values.get(v.toString()); if(pos < len && s[pos] == '!'){ res = F((int)res); pos++; } return res; } } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } long F(int n) { return n >= fif[0].length ? 0 : fif[0][n]; } public static long C(int n, int r, int mod, int[][] fif) { if (r < 0 || r > n) return 0; if(n >= fif[0].length)return 0; return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod; } public static int[][] enumFIF(int n, int mod) { int[] f = new int[n + 1]; int[] invf = new int[n + 1]; f[0] = 1; for (int i = 1; i <= n; i++) { f[i] = (int) ((long) f[i - 1] * i % mod); } long a = f[n]; long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } invf[n] = (int) (p < 0 ? p + mod : p); for (int i = n - 1; i >= 0; i--) { invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod); } return new int[][]{f, invf}; } } public static final int mod = 998244353; public void solve() { int n = ni(), m = ni(), K = ni(); var ps = new CombinationParser(998244353, 1000005); var params = Map.of("n", n, "m", m, "k", K); long D = ps.parsei("C(n,k-2)*C(m,k-2)*(k-2)!", params); long r1 = ps.parsei("C(n,k-1)*C(m,k-1)*(k-4)!*C(k-1,3)**2*9", params); long o2n = ps.parsei("C(k-2,2)*C(m-(k-2),2)*2/4 + C(k-2,2)*C(n-(k-2),2)*2/4", params); long o2v = ps.parsei("C(k-2,2)*(m-(k-2)) + C(k-2,2)*(n-(k-2))", params); long o2h = ps.parsei("(C(n,k-3)*C(m,k-3)*(k-3)!*C(m-(k-3),3)*(n-(k-3)) + C(n,k-3)*C(m,k-3)*(k-3)!*C(n-(k-3),3)*(m-(k-3)))", params); long o1n = ps.parsei("(((k-2)**2-(k-2))*(k-2-2)*(m-(k-2)) + ((k-2)**2-(k-2))*(k-2-2)*(n-(k-2)))/2", params); long o1h = ps.parsei("(((k-2)**2-(k-2))*(m-(k-2)) + ((k-2)**2-(k-2))*(n-(k-2)))/2", params); long o0n = ps.parsei("1/2*C(k-2,2)", params); long o0h = ps.parsei("2*(k-2)*C(k-3,2)", params); long o0l = ps.parsei("C(k-2,3)*3*2", params); long o0i = ps.parsei("C(k-2,2)*C(k-4,2)/2*4", params); long ans = r1 + o2n * D + o2v * D + o2h + o1n * D + o1h * D + o0n * D + o0h * D + o0l * D + o0i * D; out.println(ans%mod); } public static void main(String[] args) { new F3().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(IntUnaryOperator f, int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(f.applyAsInt(x)); } return this; } public FastWriter write(LongUnaryOperator f, long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(f.applyAsLong(x)); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); } public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); } public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); } public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }