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.io.*;
import java.util.*;

class MaxFlow {
    public class CapEdge {
        private final int from, to;
        private long cap;
        private final int rev;
        CapEdge(int from, int to, long cap, int rev) {
            this.from = from;
            this.to = to;
            this.cap = cap;
            this.rev = rev;
        }
        public int getFrom()  {return from;}
        public int getTo()    {return to;}
        public long getCap()  {return cap;}
        public long getFlow() {return g[to][rev].cap;}
    }

    private static final long INF = Long.MAX_VALUE;

    private final int n;
    private int m;
    private final java.util.ArrayList<CapEdge> edges;
    private final int[] count;
    private final CapEdge[][] g;

    public MaxFlow(int n) {
        this.n = n;
        this.edges = new java.util.ArrayList<>();
        this.count = new int[n];
        this.g = new CapEdge[n][];
    }

    public int addEdge(int from, int to, long cap) {
        rangeCheck(from, 0, n);
        rangeCheck(to, 0, n);
        nonNegativeCheck(cap, "Capacity");
        CapEdge e = new CapEdge(from, to, cap, count[to]);
        count[from]++; count[to]++;
        edges.add(e);
        return m++;
    }

    public CapEdge getEdge(int i) {
        rangeCheck(i, 0, m);
        return edges.get(i);
    }

    public java.util.ArrayList<CapEdge> getEdges() {
        return edges;
    }

    public void changeEdge(int i, long newCap, long newFlow) {
        rangeCheck(i, 0, m);
        nonNegativeCheck(newCap, "Capacity");
        if (newFlow > newCap) {
            throw new IllegalArgumentException(
                String.format("Flow %d is greater than capacity %d.", newCap, newFlow)
            );
        }
        CapEdge e = edges.get(i);
        CapEdge er = g[e.to][e.rev];
        e.cap = newCap - newFlow;
        er.cap = newFlow;
    }

    private void buildGraph() {
        for (int i = 0; i < n; i++) {
            g[i] = new CapEdge[count[i]];
        }
        int[] idx = new int[n];
        for (CapEdge e : edges) {
            g[e.to][idx[e.to]++] = new CapEdge(e.to, e.from, 0, idx[e.from]);
            g[e.from][idx[e.from]++] = e;
        }
    }

    public long maxFlow(int s, int t) {
        return flow(s, t, INF);
    }

    public long flow(int s, int t, long flowLimit) {
        rangeCheck(s, 0, n);
        rangeCheck(t, 0, n);
        buildGraph();
        long flow = 0;
        int[] level = new int[n];
        int[] que = new int[n];
        int[] iter = new int[n];
        while (true) {
            java.util.Arrays.fill(level, -1);
            dinicBFS(s, t, level, que);
            if (level[t] < 0) return flow;
            java.util.Arrays.fill(iter, 0);
            while (true) {
                long d = dinicDFS(t, s, flowLimit - flow, iter, level);
                if (d <= 0) break;
                flow += d;
            }
        }
    }

    private void dinicBFS(int s, int t, int[] level, int[] que) {
        int hd = 0, tl = 0;
        que[tl++] = s;
        level[s] = 0;
        while (tl > hd) {
            int u = que[hd++];
            for (CapEdge e : g[u]) {
                int v = e.to;
                if (e.cap <= 0 || level[v] >= 0) continue;
                level[v] = level[u] + 1;
                if (v == t) return;
                que[tl++] = v;
            }
        }
    }

    private long dinicDFS(int cur, int s, long f, int[] iter, int[] level) {
        if (cur == s) return f;
        long res = 0;
        while (iter[cur] < count[cur]) {
            CapEdge er = g[cur][iter[cur]++];
            int u = er.to;
            CapEdge e = g[u][er.rev];
            if (level[u] >= level[cur] || e.cap <= 0) continue;
            long d = dinicDFS(u, s, Math.min(f - res, e.cap), iter, level);
            if (d <= 0) continue;
            e.cap -= d;
            er.cap += d;
            res += d;
            if (res == f) break;
        }
        return res;
    }

    public long fordFulkersonMaxFlow(int s, int t) {
        return fordFulkersonFlow(s, t, INF);
    }

    public long fordFulkersonFlow(int s, int t, long flowLimit) {
        rangeCheck(s, 0, n);
        rangeCheck(t, 0, n);
        buildGraph();
        boolean[] used = new boolean[n];
        long flow = 0;
        while (true) {
            java.util.Arrays.fill(used, false);
            long f = fordFulkersonDFS(s, t, flowLimit - flow, used);
            if (f <= 0) return flow;
            flow += f;
        }
    }

    private long fordFulkersonDFS(int cur, int t, long f, boolean[] used) {
        if (cur == t) return f;
        used[cur] = true;
        for (CapEdge e : g[cur]) {
            if (used[e.to] || e.cap <= 0) continue;
            long d = fordFulkersonDFS(e.to, t, Math.min(f, e.cap), used);
            if (d <= 0) continue;
            e.cap -= d;
            g[e.to][e.rev].cap += d;
            return d;
        }
        return 0;
    }

    public boolean[] minCut(int s) {
        rangeCheck(s, 0, n);
        boolean[] reachable = new boolean[n];
        int[] stack = new int[n];
        int ptr = 0;
        stack[ptr++] = s;
        reachable[s] = true;
        while (ptr > 0) {
            int u = stack[--ptr];
            for (CapEdge e : g[u]) {
                int v = e.to;
                if (reachable[v] || e.cap <= 0) continue;
                reachable[v] = true;
                stack[ptr++] = v;
            }
        }
        return reachable;
    }

    private void rangeCheck(int i, int minInlusive, int maxExclusive) {
        if (i < 0 || i >= maxExclusive) {
            throw new IndexOutOfBoundsException(
                String.format("Index %d out of bounds for length %d", i, maxExclusive)
            );
        }
    }

    private void nonNegativeCheck(long cap, java.lang.String attribute) {
        if (cap < 0) {
            throw new IllegalArgumentException(
                String.format("%s %d is negative.", attribute, cap)
            );
        }
    }
}

public class Main {
	static int n, m;
	static char[][] f;
	static MaxFlow g;
	static void solve() {
		n = ni(); m = ni();
		f = nm(n, m);
		//頂点数が、グリッドの数と、startとgoalで、合計n * m + 2個
		g = new MaxFlow(n * m + 2);
		int s = n * m , t = s + 1;
		//sと偶数マス、tと奇数マスにエッジを張る
		for(int i=0;i<n;i++)for(int j=0;j<m;j++) {
			if(f[i][j] == '#')continue;
			int v = i * m + j;
			if((i + j) % 2 == 0) {
				g.addEdge(s, v, 1);
			}
			else {
				g.addEdge(v, t, 1);
			}
		}
		
		//偶数マス -> 奇数マス にエッジを張る
		for(int i=0;i<n;i++)for(int j=0;j<m;j++) {
			if(f[i][j] == '#')continue;
			if((i + j) % 2 == 1)continue;
			int v = i * m + j;
			addEdge(v, i, j+1);
			addEdge(v, i, j-1);
			addEdge(v, i+1, j);
			addEdge(v, i-1, j);
		}
		
		out.println(g.maxFlow(s, t));
		
		//エッジを順番に見て、マスを作成していく
		var ces = g.getEdges();
		for(var ce : ces) {
			int from = ce.getFrom(), to = ce.getTo();
			if(from == s || to == t)continue;
			if(ce.getCap() == 1)continue;
			int fi = from / m, fj = from % m;
			int ti = to / m, tj = to % m;
			if(fi == ti) {
				int min = min(fj, tj);
				int max = max(fj, tj);
				f[fi][min] = '>';
				f[fi][max] = '<';
			}
			else {
				int min = min(fi, ti);
				int max = max(fi, ti);
				f[min][fj] = 'v';
				f[max][fj] = '^';
			}
		}
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				out.print(f[i][j]);
			}
			out.println();
		}
	}	
	
	static void addEdge(int v, int ni, int nj) {
		if(ni < 0 || nj < 0)return;
		if(ni >= n || nj >= m)return;
		if(f[ni][nj] == '#')return;
		int nv = ni * m + nj;
		g.addEdge(v, nv, 1);
	}
	
 	
	//constants
	static final int inf = Integer.MAX_VALUE / 2;
	static final long linf = Long.MAX_VALUE / 3;
	static final double dinf = Double.MAX_VALUE / 3;
	static final long mod = (long) 1e9 + 7;
	static final int[] dx = { -1, 0, 1, 0 }, dy = { 0, -1, 0, 1 }, dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final double eps = 1e-10;
	
	//libraries
	static long[] cum(int a[]) {
		long[] cum = new long[a.length + 1];
		for(int i=0;i<a.length;i++) cum[i+1] = cum[i] + a[i];
		return cum;
	}
	static long[] cum(long a[]) {
		long[] cum = new long[a.length + 1];
		for(int i=0;i<a.length;i++) cum[i+1] = cum[i] + a[i];
		return cum;
	}
	static void reverse(int ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(long ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(double ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(char ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static String getReverse(String s) {
		StringBuilder sb = new StringBuilder(s);
		return sb.reverse().toString();
	}
	static <T> void reverse(T[] ar) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			T t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static int[] concat(int x, int arr[]) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}
	static int[] concat(int arr[], int x) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static long[] concat(long x, long arr[]) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}
	static long[] concat(long arr[], long x) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static char[] concat(char x, char arr[]) {
		char ret[] = new char[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static char[] concat(char arr[], char x) {
		char ret[] = new char[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static int max(int x, int y) {
		return Math.max(x, y);
	}
	static int min(int x, int y) {
		return Math.min(x, y);
	}
	static int max(int x, int y, int z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static int min(int x, int y, int z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static long max(long x, long y) {
		return Math.max(x, y);
	}
	static long min(long x, long y) {
		return Math.min(x, y);
	}
	static long max(long x, long y, long z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static long min(long x, long y, long z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static double max(double x, double y) {
		return Math.max(x, y);
	}
	static double min(double x, double y) {
		return Math.min(x, y);
	}
	static double max(double x, double y, double z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static double min(double x, double y, double z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static void sort(int[] ar) {
		Arrays.sort(ar);
	}
	static void sort(long[] ar) {
		Arrays.sort(ar);
	}
	static void sort(double[] ar) {
		Arrays.sort(ar);
	}
	static void sort(char[] ar) {
		Arrays.sort(ar);
	}
	static void rsort(int[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(long[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(double[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(char[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void fill(int arr[], int x) {
		Arrays.fill(arr, x);
	}
	static void fill(long arr[], long x) {
		Arrays.fill(arr, x);
	}
	static void fill(boolean arr[], boolean x) {
		Arrays.fill(arr, x);
	}
	static void fill(double arr[], double x) {
		Arrays.fill(arr, x);
	}
	static void fill(int arr[][], int x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(long arr[][], long x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(double arr[][], double x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(boolean arr[][], boolean x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	//MOD culc
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}
	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}
	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}
	//input
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	private static int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}
	private static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}
	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}
	@SuppressWarnings("unused")
	private static double nd() {
		return Double.parseDouble(ns());
	}
	@SuppressWarnings("unused")
	private static char nc() {
		return (char) skip();
	}
	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	@SuppressWarnings("unused")
	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}
	@SuppressWarnings("unused")
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	@SuppressWarnings("unused")
	private static long[] nla(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}
	@SuppressWarnings("unused")
	private static int[][] na(int n, int m){
		int[][] res = new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				res[i][j] = ni();
			}
		}
		return res;
	}
	@SuppressWarnings("unused")
	private static long[][] nla(int n, int m){
		long[][] res = new long[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				res[i][j] = nl();
			}
		}
		return res;
	}
	private static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	private static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
}