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.util.*;
public class sol{
    InputReader in;
    final long mod=1000000007;
    //final long mod=998244353;
    StringBuilder sb;
    public static void main(String[] args) throws java.lang.Exception{
        new sol().run();
    }
    void run() throws Exception {
        in=new InputReader(System.in);
        sb = new  StringBuilder();
        int t=1;
        while(t-->0)
            solve();
        System.out.print(sb);
    } 
    void solve() {
        int i,j, n=i(), m=i(), k=i();
        long ans=0;
        int a[]=new int[n];
        int b[]=new int[m];
        for(i=0;i<n;i++)
            a[i]=i();
        for(i=0;i<m;i++)
            b[i]=i();
        for(i=1;i<=Math.sqrt(k);i++) {
            if(k%i==0) {
                if(i<=n && (k/i)<=m) {
                    long x=0, y=0,cnt=0;
                    for(j=0;j<n;j++) {
                        if(a[j]==1)
                            cnt++;
                        else
                            cnt=0;
                        if(cnt>=i)
                            x++;
                    }
                    cnt=0;
                    for(j=0;j<m;j++) {
                        if(b[j]==1)
                            cnt++;
                        else
                            cnt=0;
                        if(cnt>=(k/i))
                            y++;
                    }
                    //System.out.println(x+" "+y);
                    ans+=x*y;
                } 
                if(i!=(k/i) && i<=m && (k/i)<=n) {
                    long x=0, y=0,cnt=0;
                    for(j=0;j<n;j++) {
                        if(a[j]==1)
                            cnt++;
                        else
                            cnt=0;
                        if(cnt>=(k/i))
                            x++;
                    }
                    cnt=0;
                    for(j=0;j<m;j++) {
                        if(b[j]==1)
                            cnt++;
                        else
                            cnt=0;
                        if(cnt>=i)
                            y++;
                    }
                    //System.out.println(x+" "+y);
                    ans+=x*y;
                } 
            }
        }
        System.out.println(ans); 
    }
    long power(long x, long y, long p) {  
        long res = 1;       
        x = x % p;  
        if (x == 0) return 0;   
        while (y > 0) {
            if((y & 1)==1) 
                res = (res * x) % p;  
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res%p; 
    } 
    int gcd(int a, int b) {
        return (b==0)?a:gcd(b,a%b);
    }
    String s(){return in.next();}
    int i(){return in.nextInt();}
    long l(){return in.nextLong();}
    class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }
        public void skip(int x) {
            while (x-->0)
                read();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public String nextString() {
            return next();
        }
        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
 
            return res.toString();
        }
        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}