import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(long M) { long x; this(in ModInt a) { x = a.x; } this(in long a) { x = a % M; if (x < 0) x += M; } ref ModInt opAssign(in long a) { return this = ModInt(a); } ref ModInt opOpAssign(string op)(in ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x *= a.x; x %= M; } else static assert(false); return this; } ref ModInt opOpAssign(string op)(in long a) { return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt opUnary(string op)() const if (op == "-") { return ModInt(-x); } ModInt opBinary(string op, T)(in T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(in long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } string toString() const { return x.to!string; } } // a^-1 (mod m) long modInv(long a, long m) in { assert(m > 0, "modInv: m > 0 must hold"); } do { long b = m, x = 1, y = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1"); if (b == -1) { y = -y; } return (y < 0) ? (y + m) : y; } x -= t * y; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1"); if (a == -1) { x = -x; } return (x < 0) ? (x + m) : x; } y -= t * x; } } enum long MO = 1000000007; alias Mint = ModInt!MO; Mint power(Mint a, long e) { Mint x = a, y = 1; for (; e; e >>= 1) { if (e & 1) y *= x; x *= x; } return y; } enum L = 2^^18; int N; long[] A; void main() { auto fft = new Fft(L); try { for (; ; ) { N = readInt(); A = new long[N]; foreach (i; 0 .. N) { A[i] = readInt(); } auto f = new real[L]; f[] = 0.0; foreach (i; 0 .. N) { f[cast(int)(A[i])] += 1; } auto ff = fft.fft(f); foreach (l; 0 .. L) { ff[l] = ff[l] * ff[l]; } auto g = fft.inverseFft(ff); auto cnt = new int[L]; foreach (l; 0 .. L) { cnt[l] = cast(int)(round(g[l].re)); } foreach (i; 0 .. N) { --cnt[cast(int)(2 * A[i])]; } cnt[] /= 2; debug { writeln("cnt = ", cnt[0 .. 20]); } return; Mint ans = 1; foreach (l; 0 .. L) { ans *= power(Mint(l), cnt[l]); } long ASum; foreach_reverse (i; 0 .. N) { ans *= power(Mint(A[i]), ASum); ASum += A[i]; } long AMin = long.max; auto opt = tuple(real.infinity, 0L, 0L); foreach_reverse (i; 0 .. N) { if (i < N - 1) { chmin(opt, tuple(log(A[i] + AMin) + log(A[i]) * AMin, A[i], AMin)); } chmin(AMin, A[i]); } debug { writeln("opt = ", opt); } Mint dnm = (opt[1] + opt[2]) * power(Mint(opt[1]), opt[2]); ans *= modInv(dnm.x, MO); writeln(ans); } } catch (EOFException e) { } }