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 PYTHON3):

Solution:
from typing import NamedTuple, Optional, List


class MaxFlow:
    class Edge(NamedTuple):
        src: int
        dst: int
        cap: int
        flow: int

    class _Edge:
        dst: int
        cap: int
        rev: Optional['MaxFlow._Edge']

        def __init__(self, dst: int, cap: int):
            self.dst = dst
            self.cap = cap
            self.rev = None

    def __init__(self, n: int):
        self._n = n
        self._g: List[List[MaxFlow._Edge]] = [[] for _ in range(n)]
        self._edges: List[MaxFlow._Edge] = []

    def add_edge(self, src: int, dst: int, cap: int) -> int:
        assert 0 <= src < self._n
        assert 0 <= dst < self._n
        assert 0 <= cap
        m = len(self._edges)
        e = MaxFlow._Edge(dst, cap)
        re = MaxFlow._Edge(src, 0)
        e.rev = re
        re.rev = e
        self._g[src].append(e)
        self._g[dst].append(re)
        self._edges.append(e)
        return m

    def get_edge(self, i: int) -> Edge:
        assert 0 <= i < len(self._edges)
        e = self._edges[i]
        re = e.rev
        return MaxFlow.Edge(
            re.dst,
            e.dst,
            e.cap + re.cap,
            re.cap
        )

    def edges(self) -> List[Edge]:
        return [self.get_edge(i) for i in range(len(self._edges))]

    def change_edge(self, i: int, new_cap: int, new_flow: int):
        assert 0 <= i < len(self._edges)
        assert 0 <= new_flow <= new_cap
        e = self._edges[i]
        e.cap = new_cap - new_flow
        e.rev.cap = new_flow

    def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> int:
        assert 0 <= s < self._n
        assert 0 <= t < self._n
        assert s != t
        if flow_limit is None:
            flow_limit = sum(e.cap for e in self._g[s])

        current_edge = [0] * self._n
        level = [0] * self._n
        buf: List[int] = []
        edge_stack: List[MaxFlow._Edge] = []

        def fill(arr: List[int], value: int):
            for i in range(len(arr)):
                arr[i] = value

        def bfs() -> bool:
            fill(level, self._n)
            queue = buf
            queue.clear()
            q_front = 0
            queue.append(s)
            level[s] = 0
            while q_front < len(queue):
                v = queue[q_front]
                q_front += 1
                next_level = level[v] + 1
                for e in self._g[v]:
                    if e.cap == 0 or level[e.dst] <= next_level:
                        continue
                    level[e.dst] = next_level
                    if e.dst == t:
                        return True
                    queue.append(e.dst)
            return False

        def dfs(lim) -> int:
            stack = buf
            stack.clear()
            stack.append(t)
            edge_stack.clear()
            while stack:
                v = stack[-1]
                if v == s:
                    flow = min(lim, min(e.cap for e in edge_stack))
                    for e in edge_stack:
                        e.cap -= flow
                        e.rev.cap += flow
                    return flow
                next_level = level[v] - 1
                while current_edge[v] < len(self._g[v]):
                    e = self._g[v][current_edge[v]]
                    re = e.rev
                    if level[e.dst] != next_level or re.cap == 0:
                        current_edge[v] += 1
                        continue
                    stack.append(e.dst)
                    edge_stack.append(re)
                    break
                else:
                    stack.pop()
                    if edge_stack:
                        edge_stack.pop()
                    level[v] = self._n
            return 0

        flow = 0
        while flow < flow_limit:
            if not bfs():
                break
            fill(current_edge, 0)
            while flow < flow_limit:
                f = dfs(flow_limit - flow)
                flow += f
                if f == 0:
                    break
        return flow


# https://atcoder.jp/contests/practice2/tasks/practice2_d
def main() -> None:
    import sys
    n, m = map(int, sys.stdin.readline().split())
    s = n * m
    t = s + 1
    g = MaxFlow(t + 1)
    grid = [list(sys.stdin.readline().strip()) for _ in range(n)]

    def enc(i: int, j: int) -> int:
        return i * m + j

    def dec(v: int) -> (int, int):
        return v // m, v % m

    for i in range(n):
        for j in range(m):
            if grid[i][j] == '#':
                continue
            if (i + j) % 2 == 0:
                g.add_edge(s, enc(i, j), 1)
            else:
                g.add_edge(enc(i, j), t, 1)

    dx = [1, 0, -1, 0]
    dy = [0, 1, 0, -1]
    for i in range(n):
        for j in range(m):
            if (i + j) % 2 == 1 or grid[i][j] == '#':
                continue
            for direction in range(4):
                ii = i + dx[direction]
                jj = j + dy[direction]
                if 0 <= ii < n and 0 <= jj < m and grid[ii][jj] == '.':
                    g.add_edge(enc(i, j), enc(ii, jj), 1)

    print(g.flow(s, t))
    for e in g.edges():
        if e.src == s or e.dst == t or e.flow == 0:
            continue
        (i, j) = dec(e.src)
        (ii, jj) = dec(e.dst)
        if i == ii + 1:
            grid[ii][jj] = 'v'
            grid[i][j] = '^'
        elif j == jj + 1:
            grid[ii][jj] = '>'
            grid[i][j] = '<'
        elif i == ii - 1:
            grid[i][j] = 'v'
            grid[ii][jj] = '^'
        else:
            grid[i][j] = '>'
            grid[ii][jj] = '<'

    for s in grid:
        print("".join(s))


if __name__ == '__main__':
    main()