Problem: ButCoder Inc. is a startup company whose main business is the development and operation of the programming competition site "ButCoder".

There are N members of the company including the president, and each member except the president has exactly one direct boss. Each member has a unique ID number from 1 to N, and the member with the ID i is called Member i. The president is Member 1, and the direct boss of Member i (2 ≤ i ≤ N) is Member b_i (1 ≤ b_i < i).

All the members in ButCoder have gathered in the great hall in the main office to take a group photo. The hall is very large, and all N people can stand in one line. However, they have been unable to decide the order in which they stand. For some reason, all of them except the president want to avoid standing next to their direct bosses.

How many ways are there for them to stand in a line that satisfy their desires? Find the count modulo 10^9+7.

Constraints

* 2 ≤ N ≤ 2000
* 1 ≤ b_i < i (2 ≤ i ≤ N)

Input

Input is given from Standard Input in the following format:


N
b_2
b_3
:
b_N


Output

Print the number of ways for the N members to stand in a line, such that no member except the president is next to his/her direct boss, modulo 10^9+7.

Examples

Input

4
1
2
3


Output

2


Input

3
1
2


Output

0


Input

5
1
1
3
3


Output

8


Input

15
1
2
3
1
4
2
7
1
8
2
8
1
8
2


Output

97193524

Solution (in CPP):

Solution:
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (1e+18) + 7;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-6;
const ld pi = acos(-1.0);
//typedef vector<vector<ll>> mat;
typedef vector<int> vec;

void debug(vector<int> &v) {
	rep(i, v.size()) {
		if (i > 0)cout << " ";
		cout << v[i];
	}
	cout << endl;
}

ll mod_pow(ll a, ll n) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * a%mod;
		a = a * a%mod; n >>= 1;
	}
	return res;
}

struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n%mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint &a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint &a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint &a, modint b) { a.n = ((ll)a.n*b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a*a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p%a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 2050;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

struct uf {
private:
	vector<int> par, ran;
public:
	uf(int n) {
		par.resize(n, 0);
		ran.resize(n, 0);
		rep(i, n) {
			par[i] = i;
		}
	}
	int find(int x) {
		if (par[x] == x)return x;
		else return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y)return;
		if (ran[x] < ran[y]) {
			par[x] = y;
		}
		else {
			par[y] = x;
			if (ran[x] == ran[y])ran[x]++;
		}
	}
	bool same(int x, int y) {
		return find(x) == find(y);
	}
};
int dx[4] = { 0,1,0,-1 };
int dy[4] = { 1,0,-1,0 };

using dp = vector<vector<modint>>;

dp merge(dp &a, dp &b) {
	int l1 = a.size();
	int l2 = b.size();
	dp res(l1 + l2 - 1);
	rep(i, l1 + l2 - 1)res[i].resize(3, 0);
	rep1(i, l1-1)rep1(j, l2-1) {
		rep(k, 3)rep(l, 3) {
			//don't connect
			res[i + j][k] += a[i][k]*b[j][l];
			//connect
			if (k<2&&l<2) {
				modint z = 1;
				if (k == 0 && l == 0)z = 2;
				if (k > 0 && l > 0)z = z / (modint)2;
				res[i + j-1][k +1] += z*a[i][k] * b[j][l];
			}
		}
	}
	return res;
}

vector<int> G[2000];

dp dfs(int id, int fr) {
	dp res(2,vector<modint>(3,0));
	res[1][0] = 1;
	for (int to : G[id]) {
		if (to == fr)continue;
		dp nex = dfs(to, id);
		res = merge(res, nex);
	}
	/*cout << "hello " << id << endl;
	rep1(i, res.size() - 1) {
		rep(j, 3) {
			cout << i << " " << j << " " << res[i][j] << endl;
		}
	}*/
	return res;
}

void solve() {
	int n; cin >> n;
	rep1(i, n-1) {
		int p; cin >> p; p--;
		G[p].push_back(i);
	}
	dp res = dfs(0, -1);
	modint ans = 0;
	rep1(i, (int)res.size()-1) {
		rep(j, 3) {
			//cout << i << " " << j << " " << res[i][j] << endl;
			modint s = res[i][j] * fact[i];
			if ((n - i) % 2)s = -s;
			ans += s;
		}
	}
	cout << ans << endl;
}


signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f(); //init();
	//init();
	//int t; cin >> t; rep(i, t)solve();
	//while(cin>>w>>h,w)solve();
	solve();
	stop
		return 0;
}