Ayrat has number n, represented as it's prime factorization pi of size m, i.e. n = p1·p2·...·pm. Ayrat got secret information that that the product of all divisors of n taken modulo 109 + 7 is the password to the secret data base. Now he wants to calculate this value.

Input

The first line of the input contains a single integer m (1 ≤ m ≤ 200 000) — the number of primes in factorization of n. 

The second line contains m primes numbers pi (2 ≤ pi ≤ 200 000).

Output

Print one integer — the product of all divisors of n modulo 109 + 7.

Examples

Input

2
2 3


Output

36


Input

3
2 3 2


Output

1728

Note

In the first sample n = 2·3 = 6. The divisors of 6 are 1, 2, 3 and 6, their product is equal to 1·2·3·6 = 36.

In the second sample 2·3·2 = 12. The divisors of 12 are 1, 2, 3, 4, 6 and 12. 1·2·3·4·6·12 = 1728.
import java.io.InputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigInteger;

public class Main{

static PrintWriter out;
static InputReader ir;

static void solve(){
 final long MOD=(long)1e9+7;
 int n=ir.nextInt();
 int[] p=ir.nextIntArray(n);
 int[] cnt=new int[200001];
 for(int i=0;i<n;i++) cnt[p[i]]++;
 BigInteger num=BigInteger.ONE;
 for(int i=0;i<=200000;i++) num=num.multiply(BigInteger.valueOf(cnt[i]+1));
 num=num.add(BigInteger.ONE);
 long mul=1;
 for(int i=0;i<n;i++) mul=mul*(long)p[i]%MOD;
 long ans=modPow(mul,num.shiftRight(1),MOD);
 if(!num.testBit(0)){
  mul=1;
  for(int i=0;i<=200000;i++){
   for(int j=0;j<(cnt[i]/2);j++){
    mul=mul*(long)i%MOD;
   }
  }
  ans=ans*mod_inverse(mul,MOD)%MOD;
 }
 out.println(ans);
}

public static long mod_inverse(long a,long MOD){
 long[] ret=extgcd(a,MOD);
 return (MOD+ret[0]%MOD)%MOD;
}

public static long[] extgcd(long a,long b){
 long[] ret=new long[3];
 ret[2]=_extgcd(a,b,ret);
 return ret;
}

private static long _extgcd(long a,long b,long[] x){
 long g=a;
 x[0]=1;
 x[1]=0;
 if(b!=0){
  g=_extgcd(b,a%b,x);
  long temp=x[0]; x[0]=x[1]; x[1]=temp;
  x[1]-=(a/b)*x[0];
 }
 return g;
}

public static long modPow(long x,BigInteger n,long MOD){
 long ret=1;
 while(n.signum()==1){
  if(n.testBit(0)) ret=ret*x%MOD;
  x=x*x%MOD;
  n=n.shiftRight(1);
 }
 return ret;
}

public static void main(String[] args) throws Exception{
 ir=new InputReader(System.in);
 out=new PrintWriter(System.out);
 solve();
 out.flush();
}

static class InputReader {
 private InputStream in;
 private byte[] buffer=new byte[1024];
 private int curbuf;
 private int lenbuf;

 public InputReader(InputStream in) {this.in=in; this.curbuf=this.lenbuf=0;}
 
 public boolean hasNextByte() {
  if(curbuf>=lenbuf){
   curbuf= 0;
   try{
    lenbuf=in.read(buffer);
   }catch(IOException e) {
    throw new InputMismatchException();
   }
   if(lenbuf<=0) return false;
  }
  return true;
 }

 private int readByte(){if(hasNextByte()) return buffer[curbuf++]; else return -1;}
 
 private boolean isSpaceChar(int c){return !(c>=33&&c<=126);}
 
 private void skip(){while(hasNextByte()&&isSpaceChar(buffer[curbuf])) curbuf++;}
 
 public boolean hasNext(){skip(); return hasNextByte();}
 
 public String next(){
  if(!hasNext()) throw new NoSuchElementException();
  StringBuilder sb=new StringBuilder();
  int b=readByte();
  while(!isSpaceChar(b)){
   sb.appendCodePoint(b);
   b=readByte();
  }
  return sb.toString();
 }
 
 public int nextInt() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  int res=0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }
 
 public long nextLong() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  long res = 0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }

 public double nextDouble(){return Double.parseDouble(next());}

 public BigInteger nextBigInteger(){return new BigInteger(next());}

 public int[] nextIntArray(int n){
  int[] a=new int[n];
  for(int i=0;i<n;i++) a[i]=nextInt();
  return a;
 }

 public long[] nextLongArray(int n){
  long[] a=new long[n];
  for(int i=0;i<n;i++) a[i]=nextLong();
  return a;
 }

 public char[][] nextCharMap(int n,int m){
  char[][] map=new char[n][m];
  for(int i=0;i<n;i++) map[i]=next().toCharArray();
  return map;
 }
}
}