import core.thread; import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.range, std.regex; // Input class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { tokens = readln.split; if (stdin.eof) throw new EOFException; } auto token = tokens[0]; tokens.popFront; return token; } int readInt() { return to!int(readToken); } long readLong() { return to!long(readToken); } real readReal() { return to!real(readToken); } // chmin/chmax void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } // Pair struct Pair(S, T) { S x; T y; int opCmp( const Pair p) const { return (x < p.x) ? -1 : (x > p.x) ? +1 : (y < p.y) ? -1 : (y > p.y) ? +1 : 0; } int opCmp(ref const Pair p) const { return (x < p.x) ? -1 : (x > p.x) ? +1 : (y < p.y) ? -1 : (y > p.y) ? +1 : 0; } string toString() const { return "(" ~ to!string(x) ~ ", " ~ to!string(y) ~ ")"; } } auto pair(S, T)(inout(S) x, inout(T) y) { return Pair!(S, T)(x, y); } // Array int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = as.length; for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) { return (a < val); }); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) { return (a <= val); }); } T[] unique(T)(in T[] as) { T[] bs; foreach (a; as) if (bs.empty || bs[$ - 1] != a) bs ~= a; return bs; } immutable long MO = 10^^9 + 7; immutable LIM = 10^^6 + 5; long[] inv, fac, facInv; int gcd(int a, int b) { return (b != 0) ? gcd(b, a % b) : a; } void main(string[] args) { inv = new long[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = MO - MO / i * inv[cast(size_t)(MO % i)] % MO; } fac = new long[LIM]; facInv = new long[LIM]; fac[0] = facInv[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i % MO; facInv[i] = facInv[i - 1] * inv[i] % MO; } try { for (; ; ) { int K = readInt; int[] C = new int[K]; foreach (k; 0 .. K) { C[k] = readInt; } const M = C.reduce!"a + b"; int[] cnt = new int[M + 1]; foreach (x; 0 .. M) { ++cnt[gcd(x, M)]; } debug{ writeln("cnt = ",cnt[1..$]); } long ans; foreach (d; 1 .. M + 1) if (cnt[d]) { bool ok = true; foreach (c; C) { ok = ok && (c % (M / d) == 0); } if (ok) { long tmp = fac[d]; foreach (c; C) { (tmp *= facInv[c / (M / d)]) %= MO; } debug{ writeln(d," ",cnt[d]," ",tmp); } (ans += cnt[d] * tmp) %= MO; } } (ans *= inv[M]) %= MO; writeln(ans); } } catch (EOFException) {} }