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.BufferedWriter;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.flush();
		out.close();
	}
}

class Pair implements Comparable<Pair> {
	int first;
	long second;
	int train;

	Pair(int first, long second, int train) {
		this.first = first;
		this.second = second;
		this.train = train;
	}

	@Override
	public int compareTo(Pair e) {
		if (second != e.second)
			return Long.compare(second, e.second);
		return train - e.train;
	}

}

class TaskB {
	long INF = (long) 1e18 + 7;
	int MAX_N = (int) 1e5 + 5;
	long mod = (long) 1e8;
	ArrayList<Pair> edges[];
	boolean processed[];
	ArrayList<Integer> topSort;
	long distTo[];
	ArrayList<Pair> trains;
	int used[];

	void dijkstra(int s) {
		PriorityQueue<Pair> queue = new PriorityQueue<>();
		queue.offer(new Pair(0, 0, 0));
		while (!queue.isEmpty()) {
			Pair temp = queue.poll();
			int u = temp.first;
			long weight = temp.second;
			int isTrain = temp.train;
			if (processed[u]) {
				continue;
			}
			processed[u] = true;
			used[u] = isTrain;
			for (Pair x : edges[u]) {
				int v = x.first;
				if (weight + x.second < distTo[v]) {
					distTo[v] = weight + x.second;
					queue.offer(new Pair(x.first, distTo[v], x.train));
				}
			}

		}
	}

	void solve(int testNumber, InputReader in, PrintWriter pw) {
		long n = in.nextInt();
		long m = in.nextInt();
		long k = in.nextInt();
		long ans = -1;
		long div1 = -1, div2 = -1;
		if (k <= n - 1) {
			long temp = k + 1;
			div1 = (n / temp) * m;
		}
		if (k <= m - 1) {
			long temp = k + 1;
			div2 = (m / temp) * n;
		}
		long div3 = -1;
		if (k >= Math.max(n - 1, m - 1) && n + m - 2 >= k) {
			k -= (Math.max(n - 1, m - 1));
			long temp = Math.min(n, m);
			div3 = temp / (k + 1);
		}
		ans = Math.max(div2, Math.max(div1, div3));
		pw.println(ans);
	}

	long gcd(long a, long b) {
		if (b == 0) {
			return a;
		} else {
			return gcd(b, a % b);
		}
	}

	int[] shrink(int a[]) {
		int n = a.length;
		long b[] = new long[n];
		for (int i = 0; i < n; i++) {
			b[i] = ((long) (a[i] << 32)) | i;
		}
		Arrays.sort(b);
		int ret[] = new int[n];
		int p = 0;
		for (int i = 0; i < n; i++) {
			if (i > 0 && (b[i] ^ b[i - 1]) >> 32 != 0) {
				p++;
			}
			ret[(int) b[i]] = p;
		}
		return ret;
	}

	int sum(int ft[], int i) {
		int sum = 0;
		for (int j = i; j >= 1; j -= (j & -j)) {
			sum += ft[j];
//			System.out.println(sum);
		}
		return sum;
	}

	void add(int ft[], int i, int x) {
		for (int j = i; j < ft.length; j += (j & -j)) {
//			System.out.println(j);
			ft[j] += x;
		}
	}

	boolean isValid(int i, int j, char arr[][]) {

		if (i >= arr[0].length || j >= arr[0].length) {
			return false;
		}
		if (arr[i][j] == '*') {
			return false;
		}
		return true;
	}

	long pow(long m, long k) {
		long prod = 1;
		for (int i = 0; i < k; i++) {
			prod = (prod * m) % INF;
		}
		return prod % INF;
	}

//	int sum(int k) {
//		int sum=0;
//		for(int i=k;i>=1;i) {
//			sum+=ft[k];
//		}
//	}

	long fib(int N) {
		long fib[] = new long[N + 1];
		fib[0] = 1;
		fib[1] = 1;
		for (int i = 2; i <= N; i++) {
			fib[i] = (fib[i - 1] + fib[i - 2]) % mod;
		}
		return fib[N] % mod;
	}

	long sum(int i, int j, long arr[]) {
		long sum = 0;
		for (int k = i; k <= j; k++) {
			sum += arr[k];
		}
		return sum;
	}

	int __gcd(int a, int b) {
		if (b == 0)
			return a;
		return __gcd(b, a % b);

	}

	public int getInt(int num) {
		int ret = -1;
		switch (num) {
		case 0:
			ret = 6;
			break;
		case 1:
			ret = 2;
			break;
		case 2:
			ret = 5;
			break;
		case 3:
			ret = 5;
			break;
		case 4:
			ret = 4;
			break;
		case 5:
			ret = 5;
			break;
		case 6:
			ret = 6;
			break;
		case 7:
			ret = 3;
			break;
		case 8:
			ret = 7;
			break;
		case 9:
			ret = 6;
			break;
		}
		return ret;
	}

	public int isPow(long num) {
		int count = 0;
		while (num > 0) {
			num /= 2;
			count++;
		}
		return count;
	}
}

class InputReader {
	BufferedReader br;
	StringTokenizer st;

	public InputReader(InputStream in) {
		br = new BufferedReader(new InputStreamReader(in));
		st = null;
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}