import std.conv, std.functional, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.range, 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)); } enum MO = 10L^^9 + 7; enum LIM = 10^^5; long[] inv, fac, invFac; void prepare() { inv = new long[LIM]; fac = new long[LIM]; invFac = new long[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = MO - ((MO / i) * inv[cast(size_t)(MO % i)]) % MO; } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = (fac[i - 1] * i) % MO; invFac[i] = (invFac[i - 1] * inv[i]) % MO; } } long binom(long n, long k) { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] % MO * invFac[cast(size_t)(n - k)] % MO; } else { return 0; } } int N; int[] A; void main() { prepare(); try { for (; ; ) { N = readInt(); A = new int[N]; foreach (i; 0 .. N) { A[i] = readInt(); } auto cnt = new int[N]; foreach (i; 0 .. N) { if (0 <= A[i] && A[i] < N) { ++cnt[A[i]]; } } auto dp = new long[N + 1]; dp[0] = 1; foreach (j; 0 .. N) { auto dpNext = new long[N + 1]; foreach (x; 0 .. N + 1) { (dpNext[x] += dp[x]) %= MO; if (x + 1 <= N) { (dpNext[x + 1] += dp[x] * cnt[j]) %= MO; } } dp = dpNext; } long ans; foreach (x; 0 .. N + 1) { ans += ((x % 2 != 0) ? -1 : +1) * dp[x] * fac[N - x]; ans %= MO; } ans = (ans % MO + MO) % MO; writeln(ans); } } catch (EOFException e) { } }