The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has n pebbles. He arranges them in a equal rows, each row has b pebbles (a > 1). Note that the Beaver must use all the pebbles he has, i. e. n = a·b.

<image> 10 pebbles are arranged in two rows, each row has 5 pebbles 

Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, b pebbles) and discards all other pebbles. Then he arranges all his pebbles again (possibly choosing other values of a and b) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. 

The game process can be represented as a finite sequence of integers c1, ..., ck, where: 

  * c1 = n
  * ci + 1 is the number of pebbles that the Beaver ends up with after the i-th move, that is, the number of pebbles in a row after some arrangement of ci pebbles (1 ≤ i < k). Note that ci > ci + 1. 
  * ck = 1



The result of the game is the sum of numbers ci. You are given n. Find the maximum possible result of the game.

Input

The single line of the input contains a single integer n — the initial number of pebbles the Smart Beaver has.

The input limitations for getting 30 points are: 

  * 2 ≤ n ≤ 50



The input limitations for getting 100 points are: 

  * 2 ≤ n ≤ 109

Output

Print a single number — the maximum possible result of the game.

Examples

Input

10


Output

16


Input

8


Output

15

Note

Consider the first example (c1 = 10). The possible options for the game development are:

  * Arrange the pebbles in 10 rows, one pebble per row. Then c2 = 1, and the game ends after the first move with the result of 11. 
  * Arrange the pebbles in 5 rows, two pebbles per row. Then c2 = 2, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. c3 = 1, and the game ends with the result of 13. 
  * Finally, arrange the pebbles in two rows, five pebbles per row. The same logic leads us to c2 = 5, c3 = 1, and the game ends with the result of 16 — the maximum possible result. 
import java.io.*;
import java.util.*;
import java.util.Queue;
import java.util.LinkedList;
import java.util.Stack;

public class Main
{
    @SuppressWarnings("unchecked")
   
      public static void main(String args[])throws IOException
    {
         Reader ob=new Reader();
        Writer out=new Writer(System.out);
        Random oo=new Random();
        long n=ob.nL();
        long h=2,sum=n;
        while(n!=1)
        {
            if(h*h>n)
            {
            sum++;
            break;
        }
        if(n%h==0)
        {
            n=n/h;
            sum+=n;
            h=2;
            
        }
        else
        h++;
        
            
        }
        out.pln(sum);
        
        out.flush();
}
static void sort(int a[])
{
    RA(a);
    Arrays.sort(a);
}
 public static int[] RA(int [] array){
		Random rgen = new Random();  // Random number generator			
 
		for (int i=0; i<array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
 
		return array;
	}
	static void sort(long a[])
{
    RA(a);
    Arrays.sort(a);
}
 public static long[] RA(long [] array){
		Random rgen = new Random();  // Random number generator			
 
		for (int i=0; i<array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
 
		return array;
	}
	static void sort(String a[])
{
    RA(a);
    Arrays.sort(a);
}
 public static String[] RA(String [] array){
		Random rgen = new Random();  // Random number generator			
 
		for (int i=0; i<array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    String temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
 
		return array;
	}
static long inverse(long x, long p)
    {
        return pow(x, p - 2, p);
    }
static boolean isPrime(long n)
{
    long h=(long)Math.sqrt(n);
    for(long i=2;i<=h;i++)
    if(n%i==0)
    return false;
    return true&&n!=1;
}
    static long gcd(long a,long b)
    {
        if(a<b)
        return gcd(b,a);
        else if(b==0)
        return a;
        else
        return gcd(b,a%b);
    }
    static long pow(long a,long b,long mod){
		if(b == 0)	return 1;
		long t = pow(a,b>>1,mod);
		t = (t * t) % mod;
		if((b & 1) == 1)	t = (t * a);
		if(t >= mod)	t %= mod;
		return t;
}
    static long pow(long a,long b){
		if(b == 0)	return 1;
		long t = pow(a,b>>1);
		t = (t * t);
		if((b & 1) == 1)	t = (t * a);
		return t;
}
    static void seive(int n,int prime[])//1 for prime -1 for not prime
    {
        for(int i=2;i<=n;i++)
            if(prime[i]==0)
            {
                prime[i]=1;
                for(int j=2;j*i<=n;j++)
                prime[j*i]=-1;
            }
    }
    static int max(int ...a)
    {
        int m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.max(m,a[i]);
        return m;
        
    }
    static long max(long ...a)
    {
        long m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.max(m,a[i]);
        return m;
    }
    static int min(int ...a)
    {
        int m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.min(m,a[i]);
        return m;
    }
    static long min(long ...a)
    {
        long m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.min(m,a[i]);
        return m;
    }
    static class Pair<T1,T2>
    {
        T1 x;T2 y;
        Pair(T1 xx,T2 yy)
        {
            x=xx;
            y=yy;
        }
    }
    
	static class Writer {
		private final PrintWriter p;
		Writer(OutputStream o) {
			p = new PrintWriter(new BufferedWriter(new OutputStreamWriter(o)));
		}
		void p(Object... o1) {
			for (Object o11 : o1) {
				p.print(o11 + "" );
			}
		}
		void p(String s) {
			p.print(s);
		}
		void pln(Object... o1) {
			p(o1);
			p.println();
		}
		void flush() {
			p.flush();
		}
		void close() {
			p.close();
		}
	}
    static class Reader {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;
		int flag=0;
		FileReader file;
		Reader()
		{
		  }
		  Reader(String x)throws IOException
		  {
		      flag=1;
		      file=new FileReader(x);
		  }
		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nl() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String n() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nL() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nI() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int[] NIA(int n) //nextINtArray
		{
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nI();
			}
			return arr;
		}
		public int[] NIA1(int n) //nextINtArray
		{
			int[] arr = new int[n+1];
			for (int i = 1; i <=n; i++) {
				arr[i] = nI();
			}
			return arr;
		}
		
		public long[] NLA(int n) //nextLongArray
		{
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nL();
			}
			return arr;
}
		public long[] NLA1(int n) //nextLongArray
		{
			long[] arr = new long[n+1];
			for (int i = 1; i <=n; i++) {
				arr[i] = nL();
			}
			return arr;
}
		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
static class DSU
{
    int a[],size[],c=1,m;
    HashMap<String,Integer> hm=new HashMap<String,Integer>();
    DSU(int n)
    {
        a=new int[n+1];
        m=n;
        size=new int[n+1];
        for(int i=1;i<=n;i++)
    {
        a[i]=i;
        size[i]=1;
    }
    }
    void add(String x,int i)
    {
        hm.put(x,i);
    }
    int find(int n)
    {
        while(a[n]!=n)
        {
            a[n]=a[a[n]];
        n=a[n];
    }
        return n;
    }
    int[] eval()
    {
       int y[]=new int[m+1];
       for(int i=1;i<=m;i++)
       y[find(i)]++;
       return y;
    }
    void union(int a1,int b)
    {
        int x=find(a1);
        int y=find(b);
        if(size[x]>size[y])
    {
        a[y]=x;
        size[x]+=size[y];
    }
    else
    {
       a[x]=y;
       size[y]+=size[x];
    }
}
        //System.out.println(Arrays.toString(a));
     int query(String x,String y)
     {
         int p=-1,q=-1;
         if(hm.containsKey(x))
         p=hm.get(x);
         else
         {
             p=c;
         hm.put(x,c++);
         
        }
         if(hm.containsKey(y))
         q=hm.get(y);
         else
         {
             q=c;
         hm.put(y,c++);
        }
        int m=find(p),n=find(q);
        if(m!=n)
        {
        union(m,n);
            return 2;
        }
        else
        return 1;
}
}
class Segment
{
    int sum[];
    void build(int a[],int v,int l,int r)
    {
        if(l==r)
        sum[v]=a[l];
        else
        {
            int m=(l+r)/2;
            build(a,v*2,l,m);
            build(a,2*v+1,m+1,r);
            sum[v]=sum[v*2]+sum[2*v+1];
        }
    }
    void update(int a[],int l,int r,int x,int v,int y)
    {
        if(l==r&&r==y)
            sum[v]+=x;
        else if(l>y||y>r)
        return;
        else
        {
            int m=(l+r)/2;
            update(a,l,m,x,2*v,y);
            update(a,m+1,r,x,2*v+1,y);
            sum[v]=sum[2*v]+sum[2*v+1];
        }
    }
    int query(int v,int l,int r,int x,int y)
    {
        if(x>r||y<l)
        return 0;
        else if(x<=l&&r<=y)
        return sum[v];
        else
        {
            int m=(l+r)/2;
        return query(2*v,l,m,x,y)+query(2*v+1,m+1,r,x,y);  
    }
}
}

static class Trie
  {
      Trie child[]=new Trie[26];
      int count=0;
    }
   /* void insert(String a)
    {
        Trie tmp=root;
        for(int i=0;i<a.length();i++)
        {
            int v=a.charAt(i)-'a';
            if(tmp.child[v]==null)
            {
                tmp.child[v]=new Trie();
                
            }
                tmp=tmp.child[v];
            }
            if(tmp.count==0)
            r++;
            tmp.count=1;
        }*/
    }
    