You are given an array a of length n and array b of length m both consisting of only integers 0 and 1. Consider a matrix c of size n × m formed by following rule: c_{i, j} = a_i ⋅ b_j (i.e. a_i multiplied by b_j). It's easy to see that c consists of only zeroes and ones too.

How many subrectangles of size (area) k consisting only of ones are there in c?

A subrectangle is an intersection of a consecutive (subsequent) segment of rows and a consecutive (subsequent) segment of columns. I.e. consider four integers x_1, x_2, y_1, y_2 (1 ≤ x_1 ≤ x_2 ≤ n, 1 ≤ y_1 ≤ y_2 ≤ m) a subrectangle c[x_1 ... x_2][y_1 ... y_2] is an intersection of the rows x_1, x_1+1, x_1+2, ..., x_2 and the columns y_1, y_1+1, y_1+2, ..., y_2.

The size (area) of a subrectangle is the total number of cells in it.

Input

The first line contains three integers n, m and k (1 ≤ n, m ≤ 40 000, 1 ≤ k ≤ n ⋅ m), length of array a, length of array b and required size of subrectangles.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 1), elements of a.

The third line contains m integers b_1, b_2, …, b_m (0 ≤ b_i ≤ 1), elements of b.

Output

Output single integer — the number of subrectangles of c with size (area) k consisting only of ones.

Examples

Input


3 3 2
1 0 1
1 1 1


Output


4


Input


3 5 4
1 1 1
1 1 1 1 1


Output


14

Note

In first example matrix c is:

<image>

There are 4 subrectangles of size 2 consisting of only ones in it:

<image>

In second example matrix c is:

<image>
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;


public class Main
{	
   static long mod=(long)(1e+9 + 7);
   //static long mod=(long)998244353;
   
   static int[] sieve;
   static ArrayList<Integer> primes;
   static PrintWriter out;
   static fast s;
   static StringBuilder fans;
  
   public static void solve()
   {
   	int n=s.nextInt();
   	int m=s.nextInt();
   	long k=s.nextLong();
  
   	int z;
//   	int a[]=new int[40000];
//   	int b[]=new int[40000];
//   	n=40000;
//   	m=40000;
//   	for(int i=0;i<a.length;i++) a[i]=1;
//   	for(int j=0;j<b.length;j++) b[j]=1;
//   	
   	int a[]=new int[n];
   	int b[]=new int[m];
   	
   	for(int i=0;i<n;i++) a[i]=s.nextInt();
   	for(int i=0;i<m;i++) b[i]=s.nextInt();
   	
   	HashMap<String,Integer> hm=new HashMap<String,Integer>();
   	StringBuilder cur=new StringBuilder("");
   	
   	for(int i=0;i<b.length;i++)
   		{
   			if(b[i]==0)
   				{
   					if(cur.length()>0)
   						hm.put(cur.toString(), hm.getOrDefault(cur.toString(),0)+1);
   					cur=new StringBuilder("");
   				}
   			else 
   				cur=cur.append(String.valueOf(b[i]));
   		}
   	
   	if(cur.length()>0)
   		hm.put(cur.toString(), hm.getOrDefault(cur.toString(),0)+1);
   	
//   	for(Map.Entry<String, Integer> mp:hm.entrySet())
//   		System.out.println(mp.getKey()+" "+mp.getValue());
//   	
   	ArrayList<Long> div=new ArrayList<Long>();
   	
   	for(long i=1;i*i<=k;i++)
   		{
   			if(k%i==0)
   				{
   					div.add(i);
   					if(k/i!=i)
   						div.add(k/i);
   				}
   		}
   
   	long cnt=0;
   	long ans=0;
   	for(int i=0;i<n;i++)
   		{
   			if(a[i]==1) cnt++;
   			else
   				{
   					for(Map.Entry<String, Integer> mp:hm.entrySet())
   						{
   							String str=mp.getKey();
   							long freq=(long)mp.getValue();
   							long len=(long)str.length();
   							
   							for(int j=0;j<div.size();j++)
   								{
   									long r=cnt-div.get(j)+1;
   									long c=len-k/div.get(j)+1;
   									
   									if(r>0 && c>0)
   								   	ans=ans+(r*c*freq);
   								}
   						}
   					cnt=0;
   				}
   		}
   	
   	if(cnt>0)
   		{
   			for(Map.Entry<String, Integer> mp:hm.entrySet())
					{
						String str=mp.getKey();
						long freq=(long)mp.getValue();
						long len=(long)str.length();
						
						for(int j=0;j<div.size();j++)
							{
								long r=cnt-div.get(j)+1;
								long c=len-k/div.get(j)+1;
								
								if(r>0 && c>0)
							   	ans=ans+(r*c*freq);
							}
					}
   		}
   	
   	System.out.println(ans);
   	
   }
   
   public static void main(String[] args) throws java.lang.Exception
   {	  	
	     s = new fast();
	     out=new PrintWriter(System.out);
	     fans=new StringBuilder("");
		    
	     
	     int t=1;
	    
	     while(t>0)
	    	 {
	    		 solve();
	    		 t--;
	    	 }
	     //System.out.println(fans);
   }
  
 
 
static class fast {   
	
	    private InputStream i;
		private byte[]  buf = new byte[1024];
		private int curChar;
		
		private int numChars;
		
		//Return floor log2n
		public static long log2(long bits) // returns 0 for bits=0
			{
			    int log = 0;
			    if( ( bits & 0xffff0000 ) != 0 ) { bits >>>= 16; log = 16; }
			    if( bits >= 256 ) { bits >>>= 8; log += 8; }
			    if( bits >= 16  ) { bits >>>= 4; log += 4; }
			    if( bits >= 4   ) { bits >>>= 2; log += 2; }
			    return log + ( bits >>> 1 );
			}
		
		public static boolean next_permutation(int a[])
		   {
			   int i=0,j=0;int index=-1;	   
			   int n=a.length;
			   
			   for(i=0;i<n-1;i++)
				   if(a[i]<a[i+1]) index=i;
			   
			   if(index==-1) return false;
			   i=index;
 
			  
			   for(j=i+1;j<n && a[i]<a[j];j++);
 
			   int temp=a[i];
			   a[i]=a[j-1];
			   a[j-1]=temp;
			   	   
			   for(int p=i+1,q=n-1;p<q;p++,q--)
			   {
				   temp=a[p];
				   a[p]=a[q];
				   a[q]=temp;
			   }
			   
			   return true;
		   }
		   
		   
		public static void division(char ch[],int divisor)
		   {
			   int div=Character.getNumericValue(ch[0]); int mul=10;int remainder=0;
			   StringBuilder quotient=new StringBuilder("");
			   for(int i=1;i<ch.length;i++)
			   {
				   div=div*mul+Character.getNumericValue(ch[i]);	
				   if(div<divisor) {quotient.append("0");continue;}
				   quotient.append(div/divisor);
				   div=div%divisor;mul=10;
				   
			   } 
			   remainder=div;
			   while(quotient.charAt(0)=='0')quotient.deleteCharAt(0);	   
			   System.out.println(quotient+" "+remainder);	  
		   }
		
		public static void sieve(int size)
		{
			sieve=new int[size+1];
			
			primes=new ArrayList<Integer>();
			
			sieve[1]=1;
			
			for(int i=2;i*i<=size;i++)
			{
				if(sieve[i]==0)
				 {
					for(int j=i*i;j<size;j+=i) {sieve[j]=1;}
				 }
			}
			
			for(int i=2;i<=size;i++)
			{
				if(sieve[i]==0) primes.add(i);
			}
		}
		
		public static long pow(long n, long b, long MOD)
		   {
		       long x=1;long y=n; 
		       while(b > 0)
		       {
		           if(b%2 == 1)
		           {
		               x=x*y;
		               if(x>MOD) x=x%(MOD);
		           }
		           y = y*y;
		           if(y>MOD) y=y%(MOD); 
		           b >>= 1;
		       }
		       return x;
		   }
 
 
		public static long mod_inv(long n,long mod)
		{
			return pow(n,mod-2,mod);
		}
		
		//Returns index of highest number less than or equal to key
		 public static int upper(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key >= a[mid]) {
		                ans=mid;
		            	low = mid+1;
		            } else if(a[mid]>key){
		                high = mid - 1;
		            }
		        }
		        return ans;
		}
		
		//Returns index of least number greater than or equal to key
		 public static int lower(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key<=a[mid]) {
		                ans=mid;
		            	high = mid-1;
		            }
		            else{
		            		low=mid+1;
		            	}
		        }
		        return ans;
		} 
		   
		public long gcd(long r,long ans)
		{
			if(r==0) return ans;
			return gcd(ans%r,r);
		}
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			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 nextString() {
     		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 nextLong() {
			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 nextInt() {
			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 boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
	}	
}