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 collections import deque

class MaxFlow:
    def __init__(self, n):
        self.n = n
        self.graph = [[] for _ in range(n)]
        self.pos = []

    def add_edge(self, fr, to, cap):
        m = len(self.pos)
        self.pos.append((fr, len(self.graph[fr])))
        self.graph[fr].append([to, len(self.graph[to]), cap])
        self.graph[to].append([fr, len(self.graph[fr]) - 1, 0])
        return m

    def get_edge(self, idx):
        to, rev, cap = self.graph[self.pos[idx][0]][self.pos[idx][1]]
        rev_to, rev_rev, rev_cap = self.graph[to][rev]
        return rev_to, to, cap + rev_cap, rev_cap

    def edges(self):
        m = len(self.pos)
        for i in range(m):
            yield self.get_edge(i)

    def change_edge(self, idx, new_cap, new_flow):
        to, rev, cap = self.graph[self.pos[idx][0]][self.pos[idx][1]]
        self.graph[self.pos[idx][0]][self.pos[idx][1]][2] = new_cap - new_flow
        self.graph[to][rev][2] = new_flow

    def dfs(self, s, v, up):
        if v == s:
            return up
        res = 0
        lv = self.level[v]
        for i in range(self.iter[v], len(self.graph[v])):
            to, rev, cap = self.graph[v][i]
            if lv <= self.level[to] or self.graph[to][rev][2] == 0:
                continue
            d = self.dfs(s, to, min(up - res, self.graph[to][rev][2]))
            if d <= 0:
                continue
            self.graph[v][i][2] += d
            self.graph[to][rev][2] -= d
            res += d
            if res == up:
                break
            self.iter[v] += 1
        return res

    def max_flow(self, s, t):
        return self.max_flow_with_limit(s, t, 2 ** 63 - 1)

    def max_flow_with_limit(self, s, t, limit):
        flow = 0
        while flow < limit:
            self.level = [-1] * self.n
            self.level[s] = 0
            queue = deque()
            queue.append(s)
            while queue:
                v = queue.popleft()
                for to, rev, cap in self.graph[v]:
                    if cap == 0 or self.level[to] >= 0:
                        continue
                    self.level[to] = self.level[v] + 1
                    if to == t:
                        break
                    queue.append(to)
            if self.level[t] == -1:
                break
            self.iter = [0] * self.n
            while flow < limit:
                f = self.dfs(s, t, limit - flow)
                if not f:
                    break
                flow += f
        return flow

    def min_cut(self, s):
        visited = [0] * self.n
        queue = deque()
        queue.append(s)
        while queue:
            p = queue.popleft()
            visited[p] = True
            for to, rev, cap in self.graph[p]:
                if cap and not visited[to]:
                    visited[to] = True
                    queue.append(to)
        return visited


n,m = map(int, input().split())
s = [list(input()) for _ in range(n)]

mf = MaxFlow(n * m + 2)

start = n * m
end = n * m + 1
d = [(1,0), (-1,0), (0,1), (0,-1)]

for i in range(n):
    for j in range(m):
        if s[i][j] == '#':
            continue
        else:
            if (i + j) % 2 == 0:
                mf.add_edge(start, i * m + j, 1)

                for i1, j1 in d:
                    if 0 <= i + i1 < n and 0 <= j + j1 < m:
                        if s[i+i1][j+j1] == '.':
                            mf.add_edge(i * m + j, (i+i1) * m + (j+j1), 1)

            else:
                mf.add_edge(i * m + j, end, 1)

print(mf.max_flow(start, end))

for i in range(len(mf.pos)):
    s1, e1, cap, flow = mf.get_edge(i)
    if flow == 0 or s1 == start or e1 == end:
        continue
    else:
        si = s1 // m
        sj = s1 % m
        ei = e1 // m
        ej = e1 % m
        if s1 - e1 == m:
            s[si][sj] = '^'
            s[ei][ej] = 'v'
        elif e1 - s1 == m:
            s[si][sj] = 'v'
            s[ei][ej] = '^'
        elif s1 - e1 == 1:
            s[si][sj] = '<'
            s[ei][ej] = '>'
        elif e1 - s1 == 1:
            s[si][sj] = '>'
            s[ei][ej] = '<'

for i in s:
    for j in i:
        print(j, end = '')
    print()