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.Arrays;

class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner();
        FastPrintStream pw = new FastPrintStream();
        solve(sc, pw);
        sc.close();
        pw.flush();
        pw.close();
    }

    public static void solve(FastScanner sc, FastPrintStream pw) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        var g = new char[n][];
        Arrays.setAll(g, i -> sc.nextChars(m));
        Digraph<CapEdge> dig = new Digraph<>(n * m + 2);
        int s = n * m;
        int t = s + 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (g[i][j] == '#') continue;
                if (((i ^ j) & 1) == 0) {
                    dig.addEdge(new CapEdge(s, i * m + j, 1));
                } else {
                    dig.addEdge(new CapEdge(i * m + j, t, 1));
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = i & 1; j < m; j += 2) {
                if (g[i][j] == '#') continue;
                if (j - 1 >= 0 && g[i][j - 1] == '.') {
                    dig.addEdge(new CapEdge(i * m + j, i * m + (j - 1), 1));
                }
                if (j + 1 < m && g[i][j + 1] == '.') {
                    dig.addEdge(new CapEdge(i * m + j, i * m + (j + 1), 1));
                }
                if (i - 1 >= 0 && g[i - 1][j] == '.') {
                    dig.addEdge(new CapEdge(i * m + j, (i - 1) * m + j, 1));
                }
                if (i + 1 < n && g[i + 1][j] == '.') {
                    dig.addEdge(new CapEdge(i * m + j, (i + 1) * m + j, 1));
                }
            }
        }
        MaxFlow mf = new MaxFlow(dig);
        int ans = (int) mf.fordFulkersonMaxFlow(s, t);
        int cnt = 0;
        for (var e : dig.getEdges()) {
            if (mf.getFlow(e) == 0) continue;
            int u = e.from;
            int v = e.to;
            if (u == s || v == t) continue;
            int ui = u / m, uj = u % m;
            int vi = v / m, vj = v % m;
            if (g[ui][uj] != '.' || g[vi][vj] != '.') {
                throw new AssertionError();
            }
            if (ui == vi) {
                if (uj + 1 == vj) {
                    g[ui][uj] = '>';
                    g[vi][vj] = '<';
                } else if (uj == vj + 1) {
                    g[ui][uj] = '<';
                    g[vi][vj] = '>';
                } else {
                    throw new AssertionError();
                }
            } else if (uj == vj) {
                if (ui + 1 == vi) {
                    g[ui][uj] = 'v';
                    g[vi][vj] = '^';
                } else if (ui == vi + 1) {
                    g[ui][uj] = '^';
                    g[vi][vj] = 'v';
                } else {
                    throw new AssertionError();
                }
            } else {
                throw new AssertionError();
            }
            cnt++;
        }
        if (ans != cnt) throw new AssertionError();
        pw.println(ans);
        for (var gi : g) {
            pw.println(gi);
        }
    }
}

class MaxFlow {
    private static final long INF = Long.MAX_VALUE;

    private final Digraph<CapEdge> dig;
    private final int n;
    private final int[] count;
    private final CapEdge[][] g;

    public MaxFlow(Digraph<CapEdge> capDiraph) {
        this.dig = capDiraph;
        this.n = capDiraph.getV();
        this.count = new int[n];
        this.g = new CapEdge[n][];
        buildGraph();
    }

    public long getFlow(CapEdge e) {
        return g[e.to][e.rev].cap;
    }

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

    private void buildGraph() {
        int[] idx = new int[n];
        for (int i = 0; i < n; i++) {
            count[i] = idx[i] = dig.deg(i);
        }
        for (CapEdge e : dig.getEdges()) {
            int j = e.to;
            count[j]++;
        }
        for (int i = 0; i < n; i++) {
            g[i] = new CapEdge[count[i]];
        }
        for (int u = 0; u < n; u++) {
            int k = dig.deg(u);
            for (int i = 0; i < k; i++) {
                CapEdge e = dig.getEdge(u, i);
                int v = e.to;
                e.rev = idx[v]++;
                CapEdge r = new CapEdge(v, u, 0);
                r.rev = i;
                g[u][i] = e;
                g[v][e.rev] = r;
            }
        }
    }

    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)
            );
        }
    }
}

abstract class AbstractGraph<Edg extends AbstractEdge> {
    final int n;
    final java.util.ArrayList<Edg> edges;
    final java.util.ArrayList<java.util.ArrayList<Edg>> adj;
    public AbstractGraph(int n) {
        this.n = n;
        this.edges = new java.util.ArrayList<>(n);
        this.adj = new java.util.ArrayList<>(n);
        for (int i = 0; i < n; i++) {
            adj.add(new java.util.ArrayList<>());
        }
    }
    public abstract void addEdge(Edg edge);
    public Edg getEdge(int u, int i) {
        return adj.get(u).get(i);
    }
    public java.util.ArrayList<Edg> getEdges(int u) {
        return adj.get(u);
    }
    public java.util.ArrayList<Edg> getEdges() {
        return edges;
    }
    public int deg(int u) {
        return adj.get(u).size();
    }
    public int getV() {
        return n;
    }
    public int getE() {
        return edges.size();
    }
}

class Graph<Edg extends AbstractEdge> extends AbstractGraph<Edg> {
    public Graph(int n) {
        super(n);
    }
    @SuppressWarnings("unchecked")
    @Override
    public void addEdge(Edg edge) {
        Edg rev = (Edg) edge.reverse();
        adj.get(edge.from).add(edge);
        adj.get(edge.to).add(rev);
        edges.add(edge);
    }
}

class Digraph<Edg extends AbstractEdge> extends AbstractGraph<Edg> {
    public Digraph(int n) {
        super(n);
    }
    @Override
    public void addEdge(Edg edge) {
        adj.get(edge.from).add(edge);
        edges.add(edge);
    }
}

abstract class AbstractEdge implements Comparable<AbstractEdge> {
    public final int from, to;
    public final long cost;
    public AbstractEdge(int from, int to, long cost) {
        this.from = from;
        this.to = to;
        this.cost = cost;
    }
    public AbstractEdge(int from, int to) {
        this(from, to, 1l);
    }
    public abstract AbstractEdge reverse();
    public int compareTo(AbstractEdge o) {
        return Long.compare(cost, o.cost);
    }
}

final class SimpleEdge extends AbstractEdge {
    public SimpleEdge(int from, int to, long cost) {
        super(from, to, cost);
    }
    public SimpleEdge(int from, int to) {
        super(from, to);
    }
    @Override
    public SimpleEdge reverse() {
        return new SimpleEdge(to, from, cost);
    }
}

final class CapEdge extends AbstractEdge {
    long cap;
    int rev;
    public CapEdge(int from, int to, long cap, long cost) {
        super(from, to, cost);
        this.cap = cap;
    }
    public CapEdge(int from, int to, long cap) {
        this(from, to, cap, 1);
    }
    @Override
    public AbstractEdge reverse() {
        throw new UnsupportedOperationException();
    }
}

class FastPrintStream implements AutoCloseable {
    private static final int BUF_SIZE = 1 << 15;
    private final byte[] buf = new byte[BUF_SIZE];
    private int ptr = 0;
    private final java.lang.reflect.Field strField;
    private final java.nio.charset.CharsetEncoder encoder;

    private java.io.OutputStream out;

    public FastPrintStream(java.io.OutputStream out) {
        this.out = out;
        java.lang.reflect.Field f;
        try {
            f = java.lang.String.class.getDeclaredField("value");
            f.setAccessible(true);
        } catch (NoSuchFieldException | SecurityException e) {
            f = null;
        }
        this.strField = f;
        this.encoder = java.nio.charset.StandardCharsets.US_ASCII.newEncoder();
    }

    public FastPrintStream(java.io.File file) throws java.io.IOException {
        this(new java.io.FileOutputStream(file));
    }

    public FastPrintStream(java.lang.String filename) throws java.io.IOException {
        this(new java.io.File(filename));
    }

    public FastPrintStream() {
        this(System.out);
        try {
            java.lang.reflect.Field f = java.io.PrintStream.class.getDeclaredField("autoFlush");
            f.setAccessible(true);
            f.set(System.out, false);
        } catch (IllegalAccessException | IllegalArgumentException | NoSuchFieldException e) {
            // ignore
        }
    }

    public FastPrintStream println() {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) '\n';
        return this;
    }

    public FastPrintStream println(java.lang.Object o) {
        return print(o).println();
    }

    public FastPrintStream println(java.lang.String s) {
        return print(s).println();
    }

    public FastPrintStream println(char[] s) {
        return print(s).println();
    }

    public FastPrintStream println(char c) {
        return print(c).println();
    }

    public FastPrintStream println(int x) {
        return print(x).println();
    }

    public FastPrintStream println(long x) {
        return print(x).println();
    }

    public FastPrintStream println(double d, int precision) {
        return print(d, precision).println();
    }

    private FastPrintStream print(byte[] bytes) {
        int n = bytes.length;
        if (ptr + n > BUF_SIZE) {
            internalFlush();
            try {
                out.write(bytes);
            } catch (java.io.IOException e) {
                throw new RuntimeException();
            }
        } else {
            System.arraycopy(bytes, 0, buf, ptr, n);
            ptr += n;
        }
        return this;
    }

    public FastPrintStream print(java.lang.Object o) {
        return print(o.toString());
    }

    public FastPrintStream print(java.lang.String s) {
        if (strField == null) {
            return print(s.getBytes());
        } else {
            try {
                return print((byte[]) strField.get(s));
            } catch (IllegalAccessException e) {
                return print(s.getBytes());
            }
        }
    }

    public FastPrintStream print(char[] s) {
        try {
            return print(encoder.encode(java.nio.CharBuffer.wrap(s)).array());
        } catch (java.nio.charset.CharacterCodingException e) {
            byte[] bytes = new byte[s.length];
            for (int i = 0; i < s.length; i++) {
                bytes[i] = (byte) s[i];
            }
            return print(bytes);
        }
    }

    public FastPrintStream print(char c) {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) c;
        return this;
    }

    public FastPrintStream print(int x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(long x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(double d, int precision) {
        if (d < 0) {
            print('-');
            d = -d;
        }
        d += Math.pow(10, -d) / 2;
        print((long) d).print('.');
        d -= (long) d;
        for(int i = 0; i < precision; i++){
            d *= 10;
            print((int) d);
            d -= (int) d;
        }
        return this;
    }

    private void internalFlush() {
        try {
            out.write(buf, 0, ptr);
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void close() {
        try {
            out.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    private static int len(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }

    private static int len(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
}

class FastScanner implements AutoCloseable {
    private final java.io.InputStream in;
    private final byte[] buf = new byte[2048];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner(java.io.InputStream in) {
        this.in = in;
    }

    public FastScanner() {
        this(System.in);
    }

    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {
            buflen = in.read(buf);
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
        return buflen > 0;
    }

    private int readByte() {
        return hasNextByte() ? buf[ptr++] : -1;
    }

    public boolean hasNext() {
        while (hasNextByte() && !(32 < buf[ptr] && buf[ptr] < 127)) ptr++;
        return hasNextByte();
    }

    private StringBuilder nextSequence() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        for (int b = readByte(); 32 < b && b < 127; b = readByte()) {
            sb.appendCodePoint(b);
        }
        return sb;
    }

    public String next() {
        return nextSequence().toString();
    }

    public String next(int len) {
        return new String(nextChars(len));
    }

    public char nextChar() {
        if (!hasNextByte()) throw new java.util.NoSuchElementException();
        return (char) readByte();
    }

    public char[] nextChars() {
        StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (32 < b && b < 127 && i < len) {
            s[i++] = (char) b; b = readByte();
        }
        if (i != len) {
            throw new java.util.NoSuchElementException(
                String.format("Next token has smaller length than expected.", len)
            );
        }
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n = n * 10 + b - '0';
            } else if (b == -1 || !(32 < b && b < 127)) {
                return minus ? -n : n;
            } else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {
        return Math.toIntExact(nextLong());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
    public void close() {
        try {
            in.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }
}