Iahub is so happy about inventing bubble sort graphs that he's staying all day long at the office and writing permutations. Iahubina is angry that she is no more important for Iahub. When Iahub goes away, Iahubina comes to his office and sabotage his research work.

The girl finds an important permutation for the research. The permutation contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n). She replaces some of permutation elements with -1 value as a revenge. 

When Iahub finds out his important permutation is broken, he tries to recover it. The only thing he remembers about the permutation is it didn't have any fixed point. A fixed point for a permutation is an element ak which has value equal to k (ak = k). Your job is to proof to Iahub that trying to recover it is not a good idea. Output the number of permutations which could be originally Iahub's important permutation, modulo 1000000007 (109 + 7).

Input

The first line contains integer n (2 ≤ n ≤ 2000). On the second line, there are n integers, representing Iahub's important permutation after Iahubina replaces some values with -1. 

It's guaranteed that there are no fixed points in the given permutation. Also, the given sequence contains at least two numbers -1 and each positive number occurs in the sequence at most once. It's guaranteed that there is at least one suitable permutation.

Output

Output a single integer, the number of ways Iahub could recover his permutation, modulo 1000000007 (109 + 7).

Examples

Input

5
-1 -1 4 3 -1


Output

2

Note

For the first test example there are two permutations with no fixed points are [2, 5, 4, 3, 1] and [5, 1, 4, 3, 2]. Any other permutation would have at least one fixed point. 
/*Author: Satyajeet Singh, Delhi Technological University*/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
 
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static boolean sieve[];
    static ArrayList<Integer> primes;
    static long factorial[],invFactorial[];
    static HashSet<Pair> graph[];
    static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
/****************************************Solutions Begins***************************************/
    static int n,k;
    static long dp[][];
    static void fact(int n){
        factorial=new long[n+1];
        invFactorial=new long [n+1];
        factorial[0]=1l;
        invFactorial[0]=1l;
        for(int i=1;i<=n;i++){
            factorial[i]=(factorial[i-1]*i)%mod;
            invFactorial[i]=modulo(factorial[i],mod-2,mod);
        }
    }
    static long ncr(int n,int k){
        long aa=invFactorial[n-k];
        long bb=invFactorial[k];
        long cc=factorial[n];
        long ans=(aa*cc)%mod;
        ans=(ans*bb)%mod;
        return ans;
    }
    static long dfs(int i,int j){
        if(j==0){
            return factorial[i];
        }
        if(j==1){
            return (i*factorial[i])%mod;
        }
        if(dp[i][j]!=-1){
            return dp[i][j];
        }
        long ans=(i*dfs(i,j-1))%mod;
        long o=((j-1)*dfs(i+1,j-2))%mod;
        ans=(ans+o)%mod;
        dp[i][j]=ans;
        return ans;
    }
    public static void main (String[] args) throws Exception {
        String st[]=nl();
        n=pi(st[0]);
        int input[]=new int[n];
        st=nl();
        HashSet<Integer> kset=new HashSet<>();
        int nk=0;
        for(int i=1;i<=n;i++){
            kset.add(i);
        }
        for(int i=0;i<n;i++){
            input[i]=pi(st[i]);
            if(input[i]==-1){
                nk++;
            }
            else{
                kset.remove(input[i]);
            }
        }
        k=0;
        for(int i=0;i<n;i++){
            if(input[i]==-1&&kset.contains(i+1)){
                k++;
            }
        }
        n=nk-k;
    //     dp=new long[nk+1][k+1];
    //     fact(100000);
    //     for(long arr[]:dp)
    //         Arrays.fill(arr,-1);
    //   //  debug(n,k);

    //     long ans=dfs(n,k);
        fact(100000);
        long ans=0;
        long sgn=1;
        for(int i=0;i<=k;i++){
            long cur=(factorial[nk-i]*ncr(k,i))%mod;
            cur*=sgn;
            ans=(ans+cur)%mod;
            ans=(ans+mod)%mod;
            sgn*=-1;
        }
        out.println(ans);
/****************************************Solutions Ends**************************************************/
        out.flush();
        out.close();
    }
/****************************************Template Begins************************************************/
    static String[] nl() throws Exception{
        return br.readLine().split(" ");
    }
    static String[] nls() throws Exception{
        return br.readLine().split("");
    }
    static int pi(String str) {
        return Integer.parseInt(str);
    }
    static long pl(String str){
        return Long.parseLong(str);
    }
    static double pd(String str){
        return Double.parseDouble(str);
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.000000000000000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static void printMask(long mask){
        System.out.println(Long.toBinaryString(mask));
    }
    static int countBit(int mask){
        int ans=0;
        while(mask!=0){
            if(mask%2==1){
                ans++;
            }
            mask/=2;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new HashSet[n];
        for(int i=0;i<n;i++){
            graph[i]=new HashSet<>();
        }
    }
    static void addEdge(int a,int b){
        graph[a].add(new Pair(b,1));
    }
    static void addEdge(int a,int b,int c){
        graph[a].add(new Pair(b,c));
    }    
/*********************************************PAIR********************************************************/
    static class PairComp implements Comparator<Pair>{
        public int compare(Pair p1,Pair p2){
            return p1.u-p2.u;
        }
    }
    static class Pair implements Comparable<Pair> {
        int u;
        int v;
        int index=-1;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public int compareTo(Pair other) {
            if(index!=other.index)
                return Long.compare(index, other.index);
            return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*******************************************************/
    static class PairCompL implements Comparator<Pairl>{
        public int compare(Pairl p1,Pairl p2){
            if(p1.u-p2.u<0){
                return -1;
            }
            else if(p1.u-p2.u>0){
                return 1;
            }
            else{
                if(p1.v-p2.v<0){
                    return -1;
                }
                else if(p1.v-p2.v>0){
                    return 1;
                }
                else{
                    return 0;
                }
            }
        }
    }
    static class Pairl implements Comparable<Pairl> {
            long u;
            long v;
            int index=-1;
            public Pairl(long u, long v) {
                this.u = u;
                this.v = v;
            }
    
            public int hashCode() {
                int hu = (int) (u ^ (u >>> 32));
                int hv = (int) (v ^ (v >>> 32));
                return 31 * hu + hv;
            }
    
            public boolean equals(Object o) {
                Pairl other = (Pairl) o;
                return u == other.u && v == other.v;
            }
    
            public int compareTo(Pairl other) {
                if(index!=other.index)
                    return Long.compare(index, other.index);
                return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
            }
    
            public String toString() {
                return "[u=" + u + ", v=" + v + "]";
            }
        }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o) {
        if(!oj)
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c) {
        long x=1;
        long y=a;
        while(b > 0){
            if(b%2 == 1){
                x=(x*y)%c;
            }
            y = (y*y)%c; // squaring the base
            b /= 2;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y)
    {
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; // a is greater number
        b = (x < y) ? x : y; // b is smaller number
        r = b;
        while(a % b != 0)
        {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
/******************************************SIEVE**********************************************************/
    static void sieveMake(int n){
        sieve=new boolean[n];
        Arrays.fill(sieve,true);
        sieve[0]=false;
        sieve[1]=false;
        for(int i=2;i*i<n;i++){
            if(sieve[i]){
                for(int j=i*i;j<n;j+=i){
                    sieve[j]=false;
                }
            }
        }
        primes=new ArrayList<Integer>();
        for(int i=0;i<n;i++){
            if(sieve[i]){
                primes.add(i);
            }
        }        
    }
/********************************************End***********************************************************/
}