import java.util.*; import java.io.*; public class Main { public static void solve(ContestScanner sc, ContestPrinter ou) { int n = sc.nextInt(); var q = new HashMap(); for (int i = 0; i < n; i++) { int d = sc.nextInt(); if (q.containsKey(d)) q.put(d, q.get(d) + 1); else q.put(d, 1); } Binom binom = new Binom(n * 2 + 2, mod); n = q.size(); var a = new Point[n]; var $ = new int[] { 0 }; q.forEach((i, j) -> { a[$[0]] = new Point(i, j); $[0]++; }); long s = 0L; for (int i = 0; i < n; i++) { long[] h = { 1L }; for (int j = 0; j < n; j++) { if (i != j) { long t = a[j].x * a[j].x - a[i].x * a[i].x; t %= mod; if (t < 0) t += mod; long[] kk = new long[a[j].y + 1]; long tt = 1; for (int k = kk.length - 1; k >= 0; k--) { kk[k] = binom.comb(a[j].y, k) * tt; kk[k] %= mod; tt *= t; tt %= mod; } h = Convolution.convolution(h, kk, mod); if (h.length > a[i].y) Arrays.copyOf(h, a[i].y); } } long inv = inv(h[0]); for (int j = 1; j < h.length; j++) { h[j - 1] = -h[j] * inv; h[j - 1] %= mod; if (h[j - 1] < 0) h[j - 1] += mod; } long[] hh = { 1L }; var ans = new long[a[i].y]; for (int k = 0; k < a[i].y; k++) { for (int l = 0; l < hh.length; l++) { ans[l] += hh[l]; ans[l] %= mod; } hh = Convolution.convolution(h, hh, mod); if (ans.length < hh.length) Arrays.copyOf(hh, ans.length); } long ss = 0L; long sss = 1L; for (int j = 0; j < ans.length; j++) { sss = binom.fact(2 * j) * binom.fact(2 * a[i].y - 2 * j - 2); sss %= mod; sss *= binom.fin(j); sss %= mod; sss *= binom.fin(a[i].y - j - 1); sss %= mod; ss += sss; ss %= mod; } ss *= binom.fin(a[i].y - 1); ss %= mod; ss *= inv; ss %= mod; ss *= inv(mp(2 * a[i].x, 2 * a[i].y - 1)); ss %= mod; s += ss; } s *= 2; s %= mod; if (s < 0) s += mod; ou.println(s); } public static int mod = 998244353; public static long inv(long a) { return mp(a, mod - 2); } public static long mp(long a, long b) { if (b == 0) return 1; if ((b & 1) == 1) return (a * mp(a, b - 1)) % mod; return mp((a * a) % mod, b >> 1); } public static void main(String[] args) { var sc = new ContestScanner(); var ou = new ContestPrinter(); solve(sc, ou); ou.flush(); ou.close(); } public static int intArray(int[] a, java.util.function.IntBinaryOperator map) { int s = a[0]; for (int i = 1; i < a.length; i++) s = map.applyAsInt(s, a[i]); return s; } public static long longArray(long[] a, java.util.function.LongBinaryOperator map) { long s = a[0]; for (int i = 1; i < a.length; i++) s = map.applyAsLong(s, a[i]); return s; } public static int max(int s, int... a) { for (int i : a) if (s < i) s = i; return s; } public static long max(long s, long... a) { for (long i : a) if (s < i) s = i; return s; } public static int min(int s, int... a) { for (int i : a) if (s > i) s = i; return s; } public static long min(long s, long... a) { for (long i : a) if (s > i) s = i; return s; } static class Point { int x; int y; Point(int x, int y) { this.x = x; this.y = y; } int compareTo(Point p) { long c = this.x - p.x; if (c < 0) return -1; if (c > 0) return 1; return 0; } boolean equals(Point p) { return this.x == p.x && this.y == p.y; } } static class Point2 { long x; int y; Point2(long x, int y) { this.x = x; this.y = y; } int compareTo(Point2 p) { long c = this.x - p.x; if (c < 0) return -1; if (c > 0) return 1; return 0; } boolean equals(Point2 p) { return this.x == p.x && this.y == p.y; } } } class Binom { private int mod; private long[] fac; private long[] fin; private long[] inv; Binom(int max, int mod) { this.mod = mod; fac = new long[max]; fin = new long[max]; inv = new long[max]; fac[0] = fac[1] = fin[0] = fin[1] = inv[1] = 1; for (int i = 2; i < max; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; fin[i] = fin[i - 1] * inv[i] % mod; } } public long comb(int n, int k) { if (n < k || n < 0 || k < 0) return 0; return fac[n] * (fin[k] * fin[n - k] % mod) % mod; } public long fact(int n) { return fac[n]; // n! を返します } public long inv(int n) { return inv[n]; // n の逆元を返します } public long fin(int n) { return fin[n]; // n! の逆元を返します } } /** * Convolution. * * @verified https://atcoder.jp/contests/practice2/tasks/practice2_f * @verified https://judge.yosupo.jp/problem/convolution_mod_1000000007 */ class Convolution { /** * Find a primitive root. * * @param m A prime number. * @return Primitive root. */ private static int primitiveRoot(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int[] divs = new int[20]; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long) (i) * i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { boolean ok = true; for (int i = 0; i < cnt; i++) { if (pow(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } /** * Power. * * @param x Parameter x. * @param n Parameter n. * @param m Mod. * @return n-th power of x mod m. */ private static long pow(long x, long n, int m) { if (m == 1) return 0; long r = 1; long y = x % m; while (n > 0) { if ((n & 1) != 0) r = (r * y) % m; y = (y * y) % m; n >>= 1; } return r; } /** * Ceil of power 2. * * @param n Value. * @return Ceil of power 2. */ private static int ceilPow2(int n) { int x = 0; while ((1L << x) < n) x++; return x; } /** * Garner's algorithm. * * @param c Mod convolution results. * @param mods Mods. * @return Result. */ private static long garner(long[] c, int[] mods) { int n = c.length + 1; long[] cnst = new long[n]; long[] coef = new long[n]; java.util.Arrays.fill(coef, 1); for (int i = 0; i < n - 1; i++) { int m1 = mods[i]; long v = (c[i] - cnst[i] + m1) % m1; v = v * pow(coef[i], m1 - 2, m1) % m1; for (int j = i + 1; j < n; j++) { long m2 = mods[j]; cnst[j] = (cnst[j] + coef[j] * v) % m2; coef[j] = (coef[j] * m1) % m2; } } return cnst[n - 1]; } /** * Pre-calculation for NTT. * * @param mod NTT Prime. * @param g Primitive root of mod. * @return Pre-calculation table. */ private static long[] sumE(int mod, int g) { long[] sum_e = new long[30]; long[] es = new long[30]; long[] ies = new long[30]; int cnt2 = Integer.numberOfTrailingZeros(mod - 1); long e = pow(g, (mod - 1) >> cnt2, mod); long ie = pow(e, mod - 2, mod); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e = e * e % mod; ie = ie * ie % mod; } long now = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_e[i] = es[i] * now % mod; now = now * ies[i] % mod; } return sum_e; } /** * Pre-calculation for inverse NTT. * * @param mod Mod. * @param g Primitive root of mod. * @return Pre-calculation table. */ private static long[] sumIE(int mod, int g) { long[] sum_ie = new long[30]; long[] es = new long[30]; long[] ies = new long[30]; int cnt2 = Integer.numberOfTrailingZeros(mod - 1); long e = pow(g, (mod - 1) >> cnt2, mod); long ie = pow(e, mod - 2, mod); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e = e * e % mod; ie = ie * ie % mod; } long now = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_ie[i] = ies[i] * now % mod; now = now * es[i] % mod; } return sum_ie; } /** * Inverse NTT. * * @param a Target array. * @param sumIE Pre-calculation table. * @param mod NTT Prime. */ private static void butterflyInv(long[] a, long[] sumIE, int mod) { int n = a.length; int h = ceilPow2(n); for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); long inow = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { long l = a[i + offset]; long r = a[i + offset + p]; a[i + offset] = (l + r) % mod; a[i + offset + p] = (mod + l - r) * inow % mod; } int x = Integer.numberOfTrailingZeros(~s); inow = inow * sumIE[x] % mod; } } } /** * Inverse NTT. * * @param a Target array. * @param sumE Pre-calculation table. * @param mod NTT Prime. */ private static void butterfly(long[] a, long[] sumE, int mod) { int n = a.length; int h = ceilPow2(n); for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); long now = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { long l = a[i + offset]; long r = a[i + offset + p] * now % mod; a[i + offset] = (l + r) % mod; a[i + offset + p] = (l - r + mod) % mod; } int x = Integer.numberOfTrailingZeros(~s); now = now * sumE[x] % mod; } } } /** * Convolution. * * @param a Target array 1. * @param b Target array 2. * @param mod NTT Prime. * @return Answer. */ public static long[] convolution(long[] a, long[] b, int mod) { int n = a.length; int m = b.length; if (n == 0 || m == 0) return new long[0]; int z = 1 << ceilPow2(n + m - 1); { long[] na = new long[z]; long[] nb = new long[z]; System.arraycopy(a, 0, na, 0, n); System.arraycopy(b, 0, nb, 0, m); a = na; b = nb; } int g = primitiveRoot(mod); long[] sume = sumE(mod, g); long[] sumie = sumIE(mod, g); butterfly(a, sume, mod); butterfly(b, sume, mod); for (int i = 0; i < z; i++) { a[i] = a[i] * b[i] % mod; } butterflyInv(a, sumie, mod); a = Arrays.copyOf(a, n + m - 1); long iz = pow(z, mod - 2, mod); for (int i = 0; i < n + m - 1; i++) a[i] = a[i] * iz % mod; return a; } /** * Convolution. * * @param a Target array 1. * @param b Target array 2. * @param mod Any mod. * @return Answer. */ public static long[] convolutionLL(long[] a, long[] b, int mod) { int n = a.length; int m = b.length; if (n == 0 || m == 0) return new long[0]; int mod1 = 754974721; int mod2 = 167772161; int mod3 = 469762049; long[] c1 = convolution(a, b, mod1); long[] c2 = convolution(a, b, mod2); long[] c3 = convolution(a, b, mod3); int retSize = c1.length; long[] ret = new long[retSize]; int[] mods = { mod1, mod2, mod3, mod }; for (int i = 0; i < retSize; ++i) { ret[i] = garner(new long[] { c1[i], c2[i], c3[i] }, mods); } return ret; } /** * Naive convolution. (Complexity is O(N^2)!!) * * @param a Target array 1. * @param b Target array 2. * @param mod Mod. * @return Answer. */ public static long[] convolutionNaive(long[] a, long[] b, int mod) { int n = a.length; int m = b.length; int k = n + m - 1; long[] ret = new long[k]; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { ret[i + j] += a[i] * b[j] % mod; ret[i + j] %= mod; } } return ret; } } class ContestScanner { private final InputStream in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; public ContestScanner(InputStream in) { this.in = in; } public ContestScanner() { this(System.in); } private boolean hasNextByte() { if (ptr < buflen) return true; ptr = 0; try { buflen = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } if (buflen <= 0) return false; return true; } private int readByte() { return hasNextByte() ? buffer[ptr++] : -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } public boolean hasNext() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } public void nextThrow(int n) { for (int i = 0; i < n; i++) this.next(); } public void nextThrow() { this.nextThrow(1); } public long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) throw new NumberFormatException(); while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) return minus ? -n : n; else throw new NumberFormatException(); b = readByte(); } } public int nextInt() { long nl = nextLong(); if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException(); return (int) nl; } public double nextDouble() { return Double.parseDouble(next()); } public boolean[] nextBoolean(char True) { String s = this.next(); int n = s.length(); boolean[] array = new boolean[n]; for (int i = 0; i < n; i++) array[i] = s.charAt(i) == True; return array; } public long[] nextLongArray(int length) { long[] array = new long[length]; for (int i = 0; i < length; i++) array[i] = this.nextLong(); return array; } public long[] nextLongArray(int length, java.util.function.LongUnaryOperator map) { long[] array = new long[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsLong(this.nextLong()); return array; } public int[] nextIntArray(int length) { int[] array = new int[length]; for (int i = 0; i < length; i++) array[i] = this.nextInt(); return array; } public int[] nextIntArray(int length, java.util.function.IntUnaryOperator map) { int[] array = new int[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsInt(this.nextInt()); return array; } public int[] nextIntArray(int length, int[] array) { int n = length + array.length; int[] a = new int[n]; for (int i = 0; i < length; i++) a[i] = this.nextInt(); for (int i = length; i < n; i++) a[i] = array[i - length]; return a; } public Integer[] nextIntegerArray(int length, java.util.function.IntUnaryOperator map) { Integer[] array = new Integer[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsInt(this.nextInt()); return array; } public Integer[] nextIntegerArray(int length) { Integer[] array = new Integer[length]; for (int i = 0; i < length; i++) array[i] = this.nextInt(); return array; } public double[] nextDoubleArray(int length) { double[] array = new double[length]; for (int i = 0; i < length; i++) array[i] = this.nextDouble(); return array; } public double[] nextDoubleArray(int length, java.util.function.DoubleUnaryOperator map) { double[] array = new double[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsDouble(this.nextDouble()); return array; } public String[] nextArray(int length) { String[] array = new String[length]; for (int i = 0; i < length; i++) array[i] = this.next(); return array; } public long[][] nextLongMatrix(int height, int width) { long[][] mat = new long[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = this.nextLong(); return mat; } public int[][] nextIntMatrix(int height, int width) { int[][] mat = new int[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = this.nextInt(); return mat; } public double[][] nextDoubleMatrix(int height, int width) { double[][] mat = new double[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = this.nextDouble(); return mat; } public boolean[][] nextBooleanMatrix(int height, int width, char True) { boolean[][] mat = new boolean[height][width]; for (int h = 0; h < height; h++) { String s = this.next(); for (int w = 0; w < width; w++) mat[h][w] = s.charAt(w) == True; } return mat; } public char[][] nextCharMatrix(int height, int width) { char[][] mat = new char[height][width]; for (int h = 0; h < height; h++) { String s = this.next(); for (int w = 0; w < width; w++) mat[h][w] = s.charAt(w); } return mat; } public char[][] nextCharMatrix(int height, int width, int h, int w, char c) { char[][] mat = new char[height + 2 * h][width + 2 * w]; for (int i = 0; i < height; i++) { String s = this.next(); for (int j = 0; j < width; j++) mat[i + h][j + w] = s.charAt(j); } for (int i = 0; i < h; i++) for (int j = 0; j < 2 * w + width; j++) mat[i][j] = c; for (int i = h + height; i < 2 * h + height; i++) for (int j = 0; j < 2 * w + width; j++) mat[i][j] = c; for (int i = h; i < h + height; i++) { for (int j = 0; j < w; j++) mat[i][j] = c; for (int j = w + width; j < 2 * w + width; j++) mat[i][j] = c; } return mat; } public boolean[][] nextBooleanMatrix(int height, int width, int h, int w, char c) { boolean[][] mat = new boolean[height + 2 * h][width + 2 * w]; for (int i = 0; i < height; i++) { String s = this.next(); for (int j = 0; j < width; j++) mat[i + h][j + w] = s.charAt(j) == c; } return mat; } } class ContestPrinter extends PrintWriter { public ContestPrinter(PrintStream stream) { super(stream); } public ContestPrinter() { super(System.out); } private static String dtos(double x, int n) { StringBuilder sb = new StringBuilder(); if (x < 0) { sb.append('-'); x = -x; } x += Math.pow(10, -n) / 2; sb.append((long) x); sb.append("."); x -= (long) x; for (int i = 0; i < n; i++) { x *= 10; sb.append((int) x); x -= (int) x; } return sb.toString(); } @Override public void print(float f) { super.print(dtos(f, 20)); } @Override public void println(float f) { super.println(dtos(f, 20)); } @Override public void print(double d) { super.print(dtos(d, 20)); } @Override public void println(double d) { super.println(dtos(d, 20)); } public void printlnArray(String[] array) { for (String i : array) super.println(i); } public void printArray(int[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printArray(int[] array) { this.printArray(array, " "); } public void printArray(Integer[] array) { this.printArray(array, " "); } public void printArray(Integer[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printlnArray(int[] array) { for (int i : array) super.println(i); } public void printArray(int[] array, String separator, java.util.function.IntUnaryOperator map) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(map.applyAsInt(array[i])); super.print(separator); } super.println(map.applyAsInt(array[n])); } public void printlnArray(int[] array, java.util.function.IntUnaryOperator map) { for (int i : array) super.println(map.applyAsInt(i)); } public void printlnArray(long[] array, java.util.function.LongUnaryOperator map) { for (long i : array) super.println(map.applyAsLong(i)); } public void printArray(int[] array, java.util.function.IntUnaryOperator map) { this.printArray(array, " ", map); } public void printArray(long[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printArray(long[] array) { this.printArray(array, " "); } public void printlnArray(long[] array) { for (long i : array) super.println(i); } public void printArray(boolean[] array, String a, String b) { int n = array.length - 1; for (int i = 0; i < n; i++) super.print((array[i] ? a : b) + " "); super.println(array[n] ? a : b); } public void printArray(boolean[] array) { this.printArray(array, "Y", "N"); } public void printArray(long[] array, String separator, java.util.function.LongUnaryOperator map) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(map.applyAsLong(array[i])); super.print(separator); } super.println(map.applyAsLong(array[n])); } public void printArray(long[] array, java.util.function.LongUnaryOperator map) { this.printArray(array, " ", map); } public void printArray(ArrayList array) { this.printArray(array, " "); } public void printArray(ArrayList array, String separator) { int n = array.size() - 1; for (int i = 0; i < n; i++) { super.print(array.get(i).toString()); super.print(separator); } super.println(array.get(n).toString()); } public void printlnArray(ArrayList array) { int n = array.size(); for (int i = 0; i < n; i++) super.println(array.get(i).toString()); } public void printArray(int[][] array) { int n = array.length; if (n == 0) return; int m = array[0].length - 1; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) super.print(array[i][j] + " "); super.println(array[i][m]); } } public void printArray(long[][] array) { int n = array.length; if (n == 0) return; int m = array[0].length - 1; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) super.print(array[i][j] + " "); super.println(array[i][m]); } } }