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 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) {
        vertexRangeCheck(from);
        vertexRangeCheck(to);
        capNonNegativeCheck(cap);
        CapEdge e = new CapEdge(from, to, cap, count[to]);
        count[from]++; count[to]++;
        edges.add(e);
        return m++;
    }

    public CapEdge getEdge(int i) {
        edgeRangeCheck(i);
        return edges.get(i);
    }

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

    public void changeEdge(int i, long newCap, long newFlow) {
        edgeRangeCheck(i);
        capNonNegativeCheck(newCap);
        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) {
        vertexRangeCheck(s);
        vertexRangeCheck(t);
        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) {
        vertexRangeCheck(s);
        vertexRangeCheck(t);
        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) {
        vertexRangeCheck(s);
        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 vertexRangeCheck(int i) {
        if (i < 0 || i >= n) {
            throw new IndexOutOfBoundsException(
                String.format("Index %d out of bounds for length %d", i, n)
            );
        }
    }

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

    private void capNonNegativeCheck(long cap) {
        if (cap < 0) {
            throw new IllegalArgumentException(
                String.format("Capacity %d is negative.", cap)
            );
        }
    }
}


public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        char[][] board = new char[N][M];
        for(int n=0; n<N; n++){
            String S = sc.next();
            for(int m=0; m<M; m++) board[n][m] = S.charAt(m);
        }

        MaxFlow G = new MaxFlow(N*M+2);
        int s = N*M, t = N*M+1;

        for(int i=0; i<N; i++) for(int j=0; j<M; j++){
            if(board[i][j] == '#') continue;
            int v = i*M+j;
            if((i+j)%2==0) G.addEdge(s, v, 1);
            else G.addEdge(v, t, 1);
        }

        for(int i=0; i<N; i++) for(int j=0; j<M; j++){
            if((i+j)%2 != 0 || board[i][j]=='#') continue;
            int v0 = i*M+j;
            if(i!=0 && board[i-1][j]=='.') G.addEdge(v0, (i-1)*M+j, 1);
            if(j!=0 && board[i][j-1]=='.') G.addEdge(v0, i*M+j-1, 1);
            if(i+1<N && board[i+1][j]=='.') G.addEdge(v0, (i+1)*M+j, 1);
            if(j+1<M && board[i][j+1]=='.') G.addEdge(v0, i*M+j+1, 1);
        }

        System.out.println(G.maxFlow(s, t));

        List<MaxFlow.CapEdge> edges = G.getEdges();
        for(MaxFlow.CapEdge e:edges){
            if(e.getFrom() == s || e.getTo() == t || e.getFlow() == 0) continue;
            int i0 = e.getFrom() / M, j0 = e.getFrom() % M, i1 = e.getTo() / M, j1 = e.getTo() % M;
            if(i0 == i1+1){
                board[i1][j1] = 'v';
                board[i0][j0] = '^';
            }else if(j0 == j1+1){
                board[i1][j1] = '>';
                board[i0][j0] = '<';
            }else if(i0 == i1-1){
                board[i0][j0] = 'v';
                board[i1][j1] = '^';
            }else{
                board[i0][j0] = '>';
                board[i1][j1] = '<';
            }
        }

        for(int n=0; n<N; n++){
            for(int m=0; m<M; m++) System.out.print(board[n][m]);
            System.out.println();
        }
        
    }
}