// ---------- begin ModInt ---------- const MOD: u32 = 1_000_000_007; #[derive(Clone, Copy)] struct ModInt(u32); impl std::ops::Add for ModInt { type Output = ModInt; fn add(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: ModInt) { *self = *self + rhs; } } impl std::ops::Sub for ModInt { type Output = ModInt; fn sub(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + MOD - rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: ModInt) { *self = *self - rhs; } } impl std::ops::Mul for ModInt { type Output = ModInt; fn mul(self, rhs: ModInt) -> Self::Output { ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32) } } impl std::ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: ModInt) { *self = *self * rhs; } } impl std::ops::Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { ModInt(if self.0 == 0 {0} else {MOD - self.0}) } } /* impl std::fmt::Display for ModInt { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.0) } } */ #[allow(dead_code)] impl ModInt { pub fn new(n: u32) -> ModInt { ModInt(n % MOD) } pub fn zero() -> ModInt { ModInt(0) } pub fn one() -> ModInt { ModInt(1) } pub fn pow(self, mut n: u32) -> ModInt { let mut t = ModInt::one(); let mut s = self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(self) -> ModInt { self.pow(MOD - 2) } pub fn comb(n: u32, k: u32) -> ModInt { if k > n { return ModInt::zero(); } let k = std::cmp::min(k, n - k); let mut nu = ModInt::one(); let mut de = ModInt::one(); for i in 0..k { nu *= ModInt(n - i); de *= ModInt(i + 1); } nu * de.inv() } } #[allow(dead_code)] struct Precalc { inv: Vec, fact: Vec, ifact: Vec, } #[allow(dead_code)] impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..(n + 1) { inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as u32); fact[i] = fact[i - 1] * ModInt(i as u32); ifact[i] = ifact[i - 1] * inv[i]; } Precalc { inv: inv, fact: fact, ifact: ifact, } } pub fn inv(&self, n: usize) -> ModInt { self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn comb(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end ModInt ---------- use std::io::Read; fn run() { let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); let mut it = s.trim().split_whitespace(); let n: usize = it.next().unwrap().parse().unwrap(); let mut cnt = vec![0; 5000]; for _ in 0..n { let k: usize = it.next().unwrap().parse().unwrap(); cnt[k] += 1; } let mut dp = vec![ModInt::one(); 1]; for i in 0..n { if cnt[i] == 0 { continue; } dp.push(ModInt::zero()); let f = ModInt(cnt[i]); for i in (0..(dp.len() - 1)).rev() { let v = dp[i]; dp[i + 1] += f * v; } } let mut ans = ModInt::zero(); let mut sign = ModInt::one(); let pc = Precalc::new(n); for (i, dp) in dp.iter().enumerate() { ans += sign * *dp * pc.fact(n - i); sign = -sign; } println!("{}", ans.0); } fn main() { run(); }