Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3 3
#..
..#
...

Sample Output 1

3
#><
vv#
^^.

The following output is also treated as a correct answer.

3
#><
v.#
^><

Solution in C++ (GCC 9.2.1 with AC Library v1.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
// #pragma GCC target("arch=skylake-avx512")
// export CPLUS_INCLUDE_PATH="/Users/shuzaei/Desktop/ac-library"
// /usr/bin/env python3 "/Users/shuzaei/Desktop/ac-library/expander.py"
// /Users/shuzaei/Desktop/Solve.cpp
#include <atcoder/maxflow>
using namespace atcoder;

#pragma region template

// Define
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <class T> using pvector = vector<pair<T, T>>;
template <class T> using rpriority_queue = priority_queue<T, vector<T>, greater<T>>;
constexpr const ll dx[4] = {1, 0, -1, 0};
constexpr const ll dy[4] = {0, 1, 0, -1};
constexpr const ll MOD = 1e9 + 7;
constexpr const ll mod = 998244353;
constexpr const ll INF = 1LL << 60;
constexpr const ll inf = 1 << 30;
constexpr const char rt = '\n';
constexpr const char sp = ' ';
#define rt(i, n) (i == (ll)(n) -1 ? rt : sp)
#define len(x) ((ll)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define ifn(x) if (not(x))
#define elif else if
#define elifn else ifn
#define fi first
#define se second
#define uniq(x) (sort(all(x)), (x).erase(unique(all(x)), (x).end()))
#define bis(x, y) ((ll)(lower_bound(all(x), y) - (x).begin()))

using graph = vector<vector<ll>>;
template <class T> using wgraph = vector<vector<pair<ll, T>>>;
bool __DIRECTED__ = true;
bool __ZERO_INDEXED__ = false;
istream &operator>>(istream &is, graph &g) {
    ll a, b;
    is >> a >> b;
    if (__ZERO_INDEXED__ == false) a--, b--;
    g[a].pb(b);
    if (__DIRECTED__ == false) g[b].pb(a);
    return is;
}
template <class T> istream &operator>>(istream &is, wgraph<T> &g) {
    ll a, b;
    T c;
    is >> a >> b >> c;
    if (__ZERO_INDEXED__ == false) a--, b--;
    g[a].pb({b, c});
    if (__DIRECTED__ == false) g[b].pb({a, c});
    return is;
}

template <class T> bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T> bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}

// Debug
#define debug(...)                                                                                 \
    {                                                                                              \
        cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ";                                         \
        for (auto &&__i : {__VA_ARGS__}) cerr << "[" << __i << "] ";                               \
        cerr << rt;                                                                                \
    }

#define dump(a, h, w)                                                                              \
    {                                                                                              \
        cerr << __LINE__ << ": " << #a << " = [" << rt;                                            \
        rep(__i, h) {                                                                              \
            rep(__j, w) {                                                                          \
                if (abs(a[__i][__j]) >= INF / 2 and a[__i][__j] <= -INF / 2) cerr << '-';          \
                if (abs(a[__i][__j]) >= INF / 2) cerr << "∞" << sp;                                \
                else                                                                               \
                    cerr << a[__i][__j] << sp;                                                     \
            }                                                                                      \
            cerr << rt;                                                                            \
        }                                                                                          \
        cerr << "]" << rt;                                                                         \
    }

#define vdump(a, n)                                                                                \
    {                                                                                              \
        cerr << __LINE__ << ": " << #a << " = [";                                                  \
        rep(__i, n) {                                                                              \
            if (__i) cerr << sp;                                                                   \
            if (abs(a[__i]) >= INF / 2 and a[__i] <= -INF / 2) cerr << '-';                        \
            if (abs(a[__i]) >= INF / 2) cerr << "∞" << sp;                                         \
            else                                                                                   \
                cerr << a[__i];                                                                    \
        }                                                                                          \
        cerr << "]" << rt;                                                                         \
    }

// Loop
#define inc(i, a, n) for (ll i = (a), _##i = (n); i <= _##i; ++i)
#define dec(i, a, n) for (ll i = (a), _##i = (n); i >= _##i; --i)
#define rep(i, n) for (ll i = 0, _##i = (n); i < _##i; ++i)
#define each(i, a) for (auto &&i : a)

// Stream
#define fout(n) cout << fixed << setprecision(n)
struct io {
    io() { cin.tie(nullptr), ios::sync_with_stdio(false); }
} io;

// Speed
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
#pragma GCC optimize("Ofast,unroll-loops")

// Math
inline constexpr ll gcd(const ll a, const ll b) { return b ? gcd(b, a % b) : a; }
inline constexpr ll lcm(const ll a, const ll b) { return a / gcd(a, b) * b; }

inline constexpr ll modulo(const ll n, const ll m = MOD) {
    ll k = n % m;
    return k + m * (k < 0);
}
inline constexpr ll chmod(ll &n, const ll m = MOD) {
    n %= m;
    return n += m * (n < 0);
}
inline constexpr ll mpow(ll a, ll n, const ll m = MOD) {
    ll r = 1;
    rep(i, 64) {
        if (n & (1LL << i)) r *= a;
        chmod(r, m);
        a *= a;
        chmod(a, m);
    }
    return r;
}
inline ll inv(const ll n, const ll m = MOD) {
    ll a = n, b = m, x = 1, y = 0;
    while (b) {
        ll t = a / b;
        a -= t * b;
        swap(a, b);
        x -= t * y;
        swap(x, y);
    }
    return modulo(x, m);
}

#pragma endregion

struct BipartiteGraph {
    ll V;
    vector<vector<ll>> G;
    vector<ll> match;
    vector<bool> used;
    BipartiteGraph(ll N) : V(N), G(N), match(N), used(N) {}
    void add_edge(ll i, ll j) {
        G[i].push_back(j);
        G[j].push_back(i);
    }
    bool dfs(ll now) {
        used[now] = true;
        rep(i, G[now].size()) {
            ll next = G[now][i], w = match[next];
            if (w == -1 || (!used[w] && dfs(w))) {
                match[now] = next, match[next] = now;
                return true;
            }
        }
        return false;
    }
    ll matching() {
        ll res = 0;
        fill(match.begin(), match.end(), -1);
        rep(i, V) {
            if (match[i] == -1) {
                fill(used.begin(), used.end(), false);
                if (dfs(i)) res++;
            }
        }
        return res;
    }
};

signed main() {
    ll N, M;
    cin >> N >> M;
    BipartiteGraph g(N * M);
    string S[N];
    rep(i, N) cin >> S[i];
    rep(i, N) rep(j, M - 1) {
        if (S[i][j] == '.' and S[i][j + 1] == '.') g.add_edge(i * M + j, i * M + j + 1);
    }
    rep(i, N - 1) rep(j, M) {
        if (S[i][j] == '.' and S[i + 1][j] == '.') g.add_edge(i * M + j, (i + 1) * M + j);
    }
    cout << g.matching() << rt;
    rep(i, len(g.match)) {
        if (g.match[i] == -1) continue;
        if (g.match[i] - i == M) {
            S[i / M][i % M] = 'v';
            S[g.match[i] / M][g.match[i] % M] = '^';
        } else if (g.match[i] - i == -M) {
            S[g.match[i] / M][g.match[i] % M] = 'v';
            S[i / M][i % M] = '^';
        } else if (g.match[i] - i == 1) {
            S[i / M][i % M] = '>';
            S[g.match[i] / M][g.match[i] % M] = '<';
        } else {
            S[g.match[i] / M][g.match[i] % M] = '>';
            S[i / M][i % M] = '<';
        }
    }
    rep(i, N) cout << S[i] << rt;
}