As we all know Barney's job is "PLEASE" and he has not much to do at work. That's why he started playing "cups and key". In this game there are three identical cups arranged in a line from left to right. Initially key to Barney's heart is under the middle cup.

<image>

Then at one turn Barney swaps the cup in the middle with any of other two cups randomly (he choses each with equal probability), so the chosen cup becomes the middle one. Game lasts n turns and Barney independently choses a cup to swap with the middle one within each turn, and the key always remains in the cup it was at the start.

After n-th turn Barney asks a girl to guess which cup contains the key. The girl points to the middle one but Barney was distracted while making turns and doesn't know if the key is under the middle cup. That's why he asked you to tell him the probability that girl guessed right.

Number n of game turns can be extremely large, that's why Barney did not give it to you. Instead he gave you an array a1, a2, ..., ak such that 

<image>

in other words, n is multiplication of all elements of the given array.

Because of precision difficulties, Barney asked you to tell him the answer as an irreducible fraction. In other words you need to find it as a fraction p / q such that <image>, where <image> is the greatest common divisor. Since p and q can be extremely large, you only need to find the remainders of dividing each of them by 109 + 7.

Please note that we want <image> of p and q to be 1, not <image> of their remainders after dividing by 109 + 7.

Input

The first line of input contains a single integer k (1 ≤ k ≤ 105) — the number of elements in array Barney gave you.

The second line contains k integers a1, a2, ..., ak (1 ≤ ai ≤ 1018) — the elements of the array.

Output

In the only line of output print a single string x / y where x is the remainder of dividing p by 109 + 7 and y is the remainder of dividing q by 109 + 7.

Examples

Input

1
2


Output

1/2


Input

3
1 1 1


Output

0/1

import static java.lang.Math.*;
import static java.util.Arrays.*;
import java.util.*;

import java.io.*;

public class Main {
	
	static final long MOD = (long)((1e9) + 7);
	static final long MOD_1 = MOD - 1;
	void solve() {
		int N = sc.nextInt();
		
		
		long n = 1;
		long parity = 1;
		for (int i = 0; i < N; i++) {
			long a = sc.nextLong();
			n = n * (a % MOD_1) % (MOD_1);
			if (a % 2 == 0) parity = 0;
		}
		
		long n_1 = (n - 1 + (MOD_1)) % (MOD_1);
		long x = mod_pow(2, n_1, MOD) % MOD;
		long y = 3 * mod_pow(2, n_1, MOD) % MOD;
		
		if (parity == 0) { x = (x + 1) % MOD; }
		else { x = (x - 1 + MOD) % MOD; }
		
		x = x * mod_inv(3, MOD) % MOD;
		y = y * mod_inv(3, MOD) % MOD;
		
		out.println(x+"/"+y);
	}
	
	long mod_pow(long a, long b, long p) {
		long res = 1;
		while (b > 0) {
			if ((b & 1) == 1)
				res = (res * a) % p;
			a = (a * a) % p;
			b >>= 1;
		}
		return res;
	}
	
	long mod_inv(long a, long p) {
	  return mod_pow(a % p, p - 2, p);
	}

	static void tr(Object... os) { System.err.println(deepToString(os)); }
	static void tr(int[][] as) { for (int[] a : as) tr(a); }

	void print(int[] a) {
		if (a.length > 0) out.print(a[0]);
		for (int i = 1; i < a.length; i++) out.print(" " + a[i]);
		out.println();
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	MyScanner sc = null;
	PrintWriter out = null;
	public void run() throws Exception {
		sc = new MyScanner(System.in);
		out = new PrintWriter(System.out);
		for (;sc.hasNext();) {
			solve();
			out.flush();
		}
		out.close();
	}

	class MyScanner {
		String line;
		BufferedReader reader;
		StringTokenizer tokenizer;

		public MyScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}
		public void eat() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					line = reader.readLine();
					if (line == null) {
						tokenizer = null;
						return;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		public String next() {
			eat();
			return tokenizer.nextToken();
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		public boolean hasNext() {
			eat();
			return (tokenizer != null && tokenizer.hasMoreElements());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
	}
}