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:
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10**9)
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10

def build_grid(H, W, intv, _type, space=False, padding=True):
    # 入力がスペース区切りかどうか
    if space:
        _input = lambda: input().split()
    else:
        _input = lambda: input()
    _list = lambda: list(map(_type, _input()))
    # 余白の有無
    if padding:
        offset = 1
    else:
        offset = 0
    grid = list2d(H+offset*2, W+offset*2, intv)
    for i in range(offset, H+offset):
        row = _list()
        for j in range(offset, W+offset):
            grid[i][j] = row[j-offset]
    return grid

class Dinic:
    """ 最大流(Dinic)：O(E*V^2) """

    INF = 10**18

    def __init__(self, n):
        self.n = n
        self.links = [[] for _ in range(n)]
        self.depth = None
        self.progress = None
        self.pos = []

    def copy(self):
        res = Dinic(self.n)
        res.links = [[a[:] for a in b] for b in self.links]
        res.pos = [a[:] for a in self.pos]
        return res

    def add_edge(self, _from, to, cap):
        self.pos.append((_from, len(self.links[_from])))
        self.links[_from].append([cap, to, len(self.links[to])])
        self.links[to].append([0, _from, len(self.links[_from]) - 1])

    def bfs(self, s):
        from collections import deque

        depth = [-1] * self.n
        depth[s] = 0
        q = deque([s])
        while q:
            v = q.popleft()
            for cap, to, _ in self.links[v]:
                if cap > 0 and depth[to] < 0:
                    depth[to] = depth[v] + 1
                    q.append(to)
        self.depth = depth

    def dfs(self, v, t, flow):
        if v == t:
            return flow
        links_v = self.links[v]
        for i in range(self.progress[v], len(links_v)):
            self.progress[v] = i
            cap, to, rev = link = links_v[i]
            if cap == 0 or self.depth[v] >= self.depth[to]:
                continue
            d = self.dfs(to, t, min(flow, cap))
            if d == 0:
                continue
            link[0] -= d
            self.links[to][rev][0] += d
            return d
        return 0

    def flow(self, s, t):
        INF = Dinic.INF
        flow = 0
        while True:
            self.bfs(s)
            if self.depth[t] < 0:
                return flow
            self.progress = [0] * self.n
            current_flow = self.dfs(s, t, INF)
            while current_flow > 0:
                flow += current_flow
                current_flow = self.dfs(s, t, INF)

    def get_edge(self, i):
        e = self.links[self.pos[i][0]][self.pos[i][1]]
        re = self.links[e[1]][e[2]]
        # from, to, cap, flow
        return (self.pos[i][0], e[1], e[0]+re[0], re[0])

    def get_edges(self):
        M = len(self.pos)
        res = []
        for i in range(M):
            res.append(self.get_edge(i))
        return res

N, M = MAP()
grid = build_grid(N, M, '#', str)
N += 2; M += 2

dinic = Dinic(N*M+2)
s = N*M
t = N*M + 1

directions = ((1, 0), (-1, 0), (0, 1), (0, -1))
for i in range(1, N-1):
    for j in range(1, M-1):
        if grid[i][j] == '#':
            continue
        u = M*i + j
        if (i+j) % 2 == 1:
            # 始点 -> 各マス
            dinic.add_edge(s, u, 1)
            for di, dj in directions:
                ni, nj = i+di, j+dj
                if grid[ni][nj] == '.':
                    v = M*ni + nj
                    # 各マス -> 4方向
                    dinic.add_edge(u, v, 1)
        else:
            # 各マス -> 終点
            dinic.add_edge(u, t, 1)

res = dinic.flow(s, t)
edges = dinic.get_edges()
for u, v, cap, f in edges:
    if u != s and v != t and f:
        ci, cj = divmod(u, M)
        ni, nj = divmod(v, M)
        if ci+1 == ni:
            grid[ci][cj] = 'v'
            grid[ni][nj] = '^'
        elif ci == ni+1:
            grid[ci][cj] = '^'
            grid[ni][nj] = 'v'
        elif cj+1 == nj:
            grid[ci][cj] = '>'
            grid[ni][nj] = '<'
        elif cj == nj+1:
            grid[ci][cj] = '<'
            grid[ni][nj] = '>'

print(res)
for i in range(1, N-1):
    print(''.join(grid[i][1:M-1]))