Jzzhu has a big rectangular chocolate bar that consists of n × m unit squares. He wants to cut this bar exactly k times. Each cut must meet the following requirements:

  * each cut should be straight (horizontal or vertical); 
  * each cut should go along edges of unit squares (it is prohibited to divide any unit chocolate square with cut); 
  * each cut should go inside the whole chocolate bar, and all cuts must be distinct. 



The picture below shows a possible way to cut a 5 × 6 chocolate for 5 times.

<image>

Imagine Jzzhu have made k cuts and the big chocolate is splitted into several pieces. Consider the smallest (by area) piece of the chocolate, Jzzhu wants this piece to be as large as possible. What is the maximum possible area of smallest piece he can get with exactly k cuts? The area of a chocolate piece is the number of unit squares in it.

Input

A single line contains three integers n, m, k (1 ≤ n, m ≤ 109; 1 ≤ k ≤ 2·109).

Output

Output a single integer representing the answer. If it is impossible to cut the big chocolate k times, print -1.

Examples

Input

3 4 1


Output

6


Input

6 4 2


Output

8


Input

2 3 4


Output

-1

Note

In the first sample, Jzzhu can cut the chocolate following the picture below:

<image>

In the second sample the optimal division looks like this:

<image>

In the third sample, it's impossible to cut a 2 × 3 chocolate 4 times.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class JzzhuandChocolate {
    static boolean test = false;

    static int n; // 10^9
    static int m; // 10^9
    static int k; // 2*10^9

    public static void main(String[] args) throws IOException {
        initReader();
        logTime("");
        while (true) {
            readInput();

            logTime("Read:");
            long result = solve();
            logTime("Solved:");

            System.out.println(result);

            if (!test)
                break;
        }

    }

    public static long solve() {
        if (k > m + n - 2)
            return -1;

        long max = 0;

        max = Math.max((long) Math.floor(n / (k + 1)) * m,
                (long) Math.floor(m / (k + 1)) * n);

        if (k >= m && k >= n) {
            max = Math.max(
                    max,
                    (long) Math.floor(n / n)
                            * (long) Math.floor(m / (k - n + 2)));
            max = Math.max(
                    max,
                    (long) Math.floor(m / m)
                            * (long) Math.floor(n / (k - m + 2)));
        }

        return max;
    }

    public static void readInput() throws IOException {
        n = nextInt();
        m = nextInt();
        k = nextInt();
    }

    /*****************************************************************
     ******************** BASIC READER *******************************
     *****************************************************************/

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    public static void initReader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static Double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    /*****************************************************************
     ******************** TIME UTILITIES *******************************
     *****************************************************************/

    static long startTime = 0;
    static long preLogTime = 0;

    static void logTime(String lable) {
        if (!test)
            return;
        long current = System.currentTimeMillis();
        if (startTime != 0) {
            println(lable, " - From start:", (current - startTime),
                    "- From previous:", (current - preLogTime));
        } else {
            startTime = current;
        }
        preLogTime = current;
    }

    /*****************************************************************
     ******************** READ UTILITIES *******************************
     *****************************************************************/

    public static int[] readArray(int n) throws IOException {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextInt();
        }
        return result;
    }

    public static long[] readArrayLong(int n) throws IOException {
        long[] result = new long[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextLong();
        }
        return result;
    }

    public static int[][] readMatrix(int row, int column) throws IOException {
        int[][] result = new int[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextInt();
            }
        }
        return result;
    }

    public static long[][] readMatrixLong(int row, int column)
            throws IOException {
        long[][] result = new long[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextLong();
            }
        }
        return result;
    }

    /*****************************************************************
     ******************** PRINT UTILITIES *******************************
     *****************************************************************/

    public static void printTest(Object... obj) {
        if (!test)
            return;
        System.out.print(join(obj, " "));
    }

    public static void printTestLn(Object... obj) {
        if (!test)
            return;
        System.out.println(join(obj, " "));
    }

    public static void print(Object... obj) {
        System.out.print(join(obj, " "));
    }

    public static void println(Object... obj) {
        System.out.println(join(obj, " "));
    }

    public static String join(Object[] objs) {
        return join(objs, " ");
    }

    public static String join(int[] objs) {
        return join(objs, " ");
    }

    public static String join(long[] objs) {
        return join(objs, " ");
    }

    public static String join(Object[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(int[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(long[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static void printMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    public static void printMatrix(long[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    /*****************************************************************
     *************** ARRAY AND STRING UTILITIES **********************
     *****************************************************************/

    public static int[] initArray(int value, int length) {
        int[] result = new int[length];
        Arrays.fill(result, value);
        return result;
    }

    public static long[] initArray(long value, int length) {
        long[] result = new long[length];
        Arrays.fill(result, value);
        return result;
    }

    public static String initString(char c, int length) {
        char[] chars = new char[length];
        Arrays.fill(chars, c);
        return new String(chars);
    }
}
