Problem: Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:

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Find the sum modulo 1073741824 (230).

Input

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 2000).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

4 4 4


Output

328


Input

10 10 10


Output

11536

Note

For the first example.

  * d(1·1·1) = d(1) = 1; 
  * d(1·1·2) = d(2) = 2; 
  * d(1·2·1) = d(2) = 2; 
  * d(1·2·2) = d(4) = 3; 
  * d(2·1·1) = d(2) = 2; 
  * d(2·1·2) = d(4) = 3; 
  * d(2·2·1) = d(4) = 3; 
  * d(2·2·2) = d(8) = 4. 



So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20.

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;
 
public class Main
{
	//Fast IO class
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
        public FastReader() 
        { 
        	boolean env=System.getProperty("ONLINE_JUDGE") != null;
        	if(!env) {
        		try {
					br=new BufferedReader(new FileReader("src\\input.txt"));
				} catch (FileNotFoundException e) {
					e.printStackTrace();
				}
        	}
        	else {
        		br = new BufferedReader(new
                        InputStreamReader(System.in)); 
        	}
        } 
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }     
    static long MOD=1000000000+7;
    //Euclidean Algorithm
    static long gcd(long A,long B){
        if(B==0) return A;
        return gcd(B,A%B);
    }
    //Modular Exponentiation
    static long fastExpo(long x,long n){
        if(n==0) return 1;
        if((n&1)==0) return fastExpo((x*x)%MOD,n/2)%MOD;
        return ((x%MOD)*fastExpo((x*x)%MOD,(n-1)/2))%MOD;
    }
    //Prime Number Algorithm
    static boolean isPrime(long n){
        if(n<=1) return false;
        if(n<=3) return true;
        if(n%2==0 || n%3==0) return false;
        for(int i=5;i*i<=n;i+=6)
            if(n%i==0 || n%(i+2)==0) return false;
        return true;
    }
    //Sieve of eratosthenes
    static int[] findPrimes(int n){
        boolean isPrime[]=new boolean[n+1];
        ArrayList<Integer> a=new ArrayList<>();
        int result[];
        Arrays.fill(isPrime,true);
        isPrime[0]=false;
        isPrime[1]=false;
        for(int i=2;i*i<=n;++i)
            if(isPrime[i]==true)
                for(int j=i*i;j<=n;j+=i) isPrime[j]=false;
        for(int i=0;i<=n;i++) if(isPrime[i]==true) a.add(i);
        result=new int[a.size()];
        for(int i=0;i<a.size();i++) result[i]=a.get(i);
        return result;
    } 
    // Pair
    static class pair{
    	double x,y;
    	pair(double a,double b){
    		this.x=a;
    		this.y=b;
    	}
    	public boolean equals(Object obj) {
    		if(obj == null || obj.getClass()!= this.getClass()) 
                return false;
            pair p = (pair) obj;
            return (this.x==p.x && this.y==p.y);
        }
    	public int hashCode() {
            return Objects.hash(x, y);
        }
    }
    //Main function(The main code starts from here)
    static long div(long x) {
    	long cnt=0;
    	for(int i=1;i*i<=x;i++) {
    		if(x%i==0) {
    			cnt++;
    			if(i*i!=x) cnt++;
    		}
    	}
    	return cnt%MOD;
    }
    static long dp[]=new long[1000000+1];
    public static void main (String[] args) throws java.lang.Exception
    {
        FastReader sc=new FastReader();
    	int test=1;
        while(test-->0) {
        	MOD=1073741824;
        	int a=sc.nextInt(),b=sc.nextInt(),c=sc.nextInt();
        	long ans=0;
        	for(int i=1;i<=a;i++) 
        		for(int j=1;j<=b;j++) 
        			for(int k=1;k<=c;k++) {
        				if(dp[i*j*k]==0) dp[i*j*k]=div(i*j*k);
        				ans=(ans%MOD+dp[i*j*k]%MOD)%MOD;
        			}
        	System.out.println(ans);
        }
    }
}