Problem: You are given a grid of N rows and M columns. The square at the i-th row and j-th column will be denoted as (i,j). Some of the squares contain an object. All the remaining squares are empty. The state of the grid is represented by strings S_1,S_2,\cdots,S_N. The square (i,j) contains an object if S_{i,j}= `#` and is empty if S_{i,j}= `.`.

Consider placing 1 \times 2 tiles on the grid. Tiles can be placed vertically or horizontally to cover two adjacent empty squares. Tiles must not stick out of the grid, and no two different tiles may intersect. Tiles cannot occupy the square with an object.

Calculate the maximum number of tiles that can be placed and any configulation that acheives the maximum.

Constraints

* 1 \leq N \leq 100
* 1 \leq M \leq 100
* S_i is a string with length M consists of `#` and `.`.

Input

Input is given from Standard Input in the following format:


N M
S_1
S_2
\vdots
S_N


Output

On the first line, print the maximum number of tiles that can be placed.

On the next N lines, print a configulation that achieves the maximum. Precisely, output the strings t_1,t_2,\cdots,t_N constructed by the following way.

* t_i is initialized to S_i.
* For each (i,j), if there is a tile that occupies (i,j) and (i+1,j), change t_{i,j}:=`v`, t_{i+1,j}:=`^`.
* For each (i,j), if there is a tile that occupies (i,j) and (i,j+1), change t_{i,j}:=`>`, t_{i,j+1}:=`<`.



See samples for further information.

You may print any configulation that maximizes the number of tiles.

Examples

Input

3 3
#..
..#
...


Output

3
#><
vv#
^^.


Input

3 3
..
..#
...


Output

3
><
vv#
^^.

Solution (in JAVA):

Solution:
import java.util.*;

class MaxFlow4 {
	public static class Edge {
		public int from, to;
		public int capacity;
		public int flow;
		public Edge complement;
		public boolean cloned;

		public Edge(int from, int to, int capacity) {
			this.from = from;
			this.to = to;
			this.capacity = capacity;
		}
	}

	public static void reset(Edge[][] g) {
		for (Edge[] row : g) {
			for (Edge e : row) {
				e.flow = e.cloned ? e.capacity : 0;
			}
		}
	}

	public static Edge[][] compileWD(int n, List<Edge> edges) {
		Edge[][] g = new Edge[n][];
		// cloning
		for (int i = edges.size() - 1; i >= 0; i--) {
			Edge origin = edges.get(i);
			Edge clone = new Edge(origin.to, origin.from, origin.capacity);
			clone.flow = origin.capacity;
			clone.complement = origin;
			clone.cloned = true;
			origin.complement = clone;
			edges.add(clone);
		}

		int[] p = new int[n];
		for (Edge e : edges)
			p[e.from]++;
		for (int i = 0; i < n; i++)
			g[i] = new Edge[p[i]];
		for (Edge e : edges)
			g[e.from][--p[e.from]] = e;
		return g;
	}

	public static Edge[][] compileWU(int n, List<Edge> edges) {
		Edge[][] g = new Edge[n][];
		// cloning
		for (int i = edges.size() - 1; i >= 0; i--) {
			Edge origin = edges.get(i);
			Edge clone = new Edge(origin.to, origin.from, origin.capacity * 2);
			origin.flow = origin.capacity;
			clone.flow = origin.capacity;
			clone.complement = origin;
			clone.cloned = true;
			origin.complement = clone;
			origin.capacity *= 2;
			edges.add(clone);
		}

		int[] p = new int[n];
		for (Edge e : edges)
			p[e.from]++;
		for (int i = 0; i < n; i++)
			g[i] = new Edge[p[i]];
		for (Edge e : edges)
			g[e.from][--p[e.from]] = e;
		return g;
	}

	public static long maximumFlowDinic(Edge[][] g, int source, int sink) {
		int n = g.length;
		int[] d = new int[n];
		int[] q = new int[n];
		long ret = 0;
		while (true) {
			Arrays.fill(d, -1);
			q[0] = source;
			int r = 1;
			d[source] = 0;

			for (int v = 0; v < r; v++) {
				int cur = q[v];
				for (Edge ne : g[cur]) {
					if (d[ne.to] == -1 && ne.capacity - ne.flow > 0) {
						q[r++] = ne.to;
						d[ne.to] = d[cur] + 1;
					}
				}
			}
			if (d[sink] == -1)
				break;
			int[] sp = new int[n];
			for (int i = 0; i < n; i++)
				sp[i] = g[i].length - 1;
			ret += dfsDinic(d, g, sp, source, sink, Long.MAX_VALUE);
		}

		return ret;
	}

	private static long dfsDinic(int[] d, Edge[][] g, int[] sp, int cur, int sink, long min) {
		if (cur == sink)
			return min;
		long left = min;
		for (int i = sp[cur]; i >= 0; i--) {
			Edge ne = g[cur][i];
			if (d[ne.to] == d[cur] + 1 && ne.capacity - ne.flow > 0) {
				long fl = dfsDinic(d, g, sp, ne.to, sink, Math.min(left, ne.capacity - ne.flow));
				if (fl > 0) {
					left -= fl;
					ne.flow += fl;
					ne.complement.flow -= fl;
					if (left == 0) {
						sp[cur] = i;
						return min;
					}
				}
			}
		}
		sp[cur] = -1;
		return min - left;
	}
}

@SuppressWarnings("unused")
public class Main {

	private static void solve() {
		int h = ni();
		int w = ni();
		char[][] map = new char[h][w];
		for (int i = 0; i < h; i++) {
			map[i] = ns();
		}

		List<MaxFlow4.Edge> edges = new ArrayList<>();
		int src = h * w;
		int sink = h * w + 1;
		int n = h * w + 2;

		int[][] dir = { { 0, 1 }, { 1, 0 }, { -1, 0 }, { 0, -1 } };
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				int v = i * w + j;
				if (map[i][j] == '#')
					continue;
				if ((i + j) % 2 == 0) {
					edges.add(new MaxFlow4.Edge(src, v, 1));
					for (int[] d : dir) {
						int ni = i + d[0];
						int nj = j + d[1];
						if (0 <= ni && ni < h && 0 <= nj && nj < w) {
							if (map[ni][nj] == '#')
								continue;
							edges.add(new MaxFlow4.Edge(v, ni * w + nj, 1));
						}
					}
				} else {
					edges.add(new MaxFlow4.Edge(v, sink, 1));
				}
			}
		}
		MaxFlow4.Edge[][] g = MaxFlow4.compileWD(n, edges);
		long ret = MaxFlow4.maximumFlowDinic(g, src, sink);

		for (MaxFlow4.Edge e : edges) {
			if (e.cloned != false &&  e.flow == 0 && e.from != src && e.from != sink && e.to != src && e.to != sink) {
				int a = Math.min(e.from, e.to);
				int b = Math.max(e.from, e.to);
				if (w >= 2 && b - a == 1) {
					map[a/w][a%w] = '>';
					map[b/w][b%w] = '<';
				} else {
					map[a/w][a%w] = 'v';
					map[b/w][b%w] = '^';
				}
			}
		}
		System.out.println(ret);
		for (char[] line : map) {
			System.out.println(line);
		}
	}

	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			@Override
			public void run() {
				long start = System.currentTimeMillis();
				String debug = args.length > 0 ? args[0] : null;
				if (debug != null) {
					try {
						is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
					} catch (Exception e) {
						throw new RuntimeException(e);
					}
				}
				reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
				solve();
				out.flush();
				tr((System.currentTimeMillis() - start) + "ms");
			}
		}, "", 64000000).start();
	}

	private static java.io.InputStream is = System.in;
	private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
	private static java.util.StringTokenizer tokenizer = null;
	private static java.io.BufferedReader reader;

	public static String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new java.util.StringTokenizer(reader.readLine());
			} catch (Exception e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	private static double nd() {
		return Double.parseDouble(next());
	}

	private static long nl() {
		return Long.parseLong(next());
	}

	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private static char[] ns() {
		return next().toCharArray();
	}

	private static long[] nal(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private static int[][] ntable(int n, int m) {
		int[][] table = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				table[i][j] = ni();
			}
		}
		return table;
	}

	private static int[][] nlist(int n, int m) {
		int[][] table = new int[m][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				table[j][i] = ni();
			}
		}
		return table;
	}

	private static int ni() {
		return Integer.parseInt(next());
	}

	private static void tr(Object... o) {
		if (is != System.in)
			System.out.println(java.util.Arrays.deepToString(o));
	}
}