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). A nonnegative integer A_{i,j} is written for each square (i,j).

You choose some of the squares so that each row and column contains at most K chosen squares. Under this constraint, calculate the maximum value of the sum of the integers written on the chosen squares. Additionally, calculate a way to choose squares that acheives the maximum.

Constraints

* 1 \leq N \leq 50
* 1 \leq K \leq N
* 0 \leq A_{i,j} \leq 10^9
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N K
A_{1,1} A_{1,2} \cdots A_{1,N}
A_{2,1} A_{2,2} \cdots A_{2,N}
\vdots
A_{N,1} A_{N,2} \cdots A_{N,N}


Output

On the first line, print the maximum value of the sum of the integers written on the chosen squares.

On the next N lines, print a way that achieves the maximum.

Precisely, output the strings t_1,t_2,\cdots,t_N, that satisfies t_{i,j}=`X` if you choose (i,j) and t_{i,j}=`.` otherwise.

You may print any way to choose squares that maximizes the sum.

Examples

Input

3 1
5 3 2
1 4 8
7 6 9


Output

19
X..
..X
.X.


Input

3 2
10 10 1
10 10 1
1 1 10


Output

50
XX.
XX.
..X

Solution (in CPP):

Solution:
/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2020.09.09 18:09:43
**/

#include "bits/stdc++.h" 
using namespace std; 
typedef long long ll;


template <typename Cap, typename Cost>
struct MininumCostFlow {
private:
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };
    int _n; 
    std::vector<std::pair<int, int>> pos; 
    std::vector<std::vector<_edge>> g;
public:
    MininumCostFlow() {}
    
    MininumCostFlow(int n) : _n(n), g(n) {}
    
    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        g[from].push_back(_edge{to, int(g[to].size()), cap, cost});
        g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost});
        return m;
    }
    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };
    
    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{
            pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,
        };
    }
    
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result(m);
        for (int i = 0; i < m; i++) {
            result[i] = get_edge(i);
        }
        return result;
    }
    
    std::pair<Cap, Cost> flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    
    std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
        return slope(s, t, flow_limit).back();
    }
    
    std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
        return slope(s, t, std::numeric_limits<Cap>::max());
    }
    
    std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
        std::vector<Cost> dual(_n, 0), dist(_n);
        std::vector<int> pv(_n), pe(_n);
        std::vector<bool> vis(_n);
        auto dual_ref = [&]() {
            std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
            std::fill(pv.begin(), pv.end(), -1);
            std::fill(pe.begin(), pe.end(), -1);
            std::fill(vis.begin(), vis.end(), false);
            struct Q {
                Cost key;
                int to;
                bool operator<(Q r) const { return key > r.key; }
            };
            std::priority_queue<Q> que;
            dist[s] = 0;
            que.push(Q{0, s});
            while (!que.empty()) {
                int v = que.top().to;
                que.pop();
                if (vis[v]) continue;
                vis[v] = true;
                if (v == t) break;
                for (int i = 0; i < int(g[v].size()); i++) {
                    auto e = g[v][i];
                    if (vis[e.to] || !e.cap) continue;
                    Cost cost = e.cost - dual[e.to] + dual[v];
                    if (dist[e.to] - dist[v] > cost) {
                        dist[e.to] = dist[v] + cost;
                        pv[e.to] = v;
                        pe[e.to] = i;
                        que.push(Q{dist[e.to], e.to});
                    }
                }
            }
            if (!vis[t]) {
                return false;
            }
            for (int v = 0; v < _n; v++) {
                if (!vis[v]) continue;
                dual[v] -= dist[t] - dist[v];
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost = -1;
        std::vector<std::pair<Cap, Cost>> result;
        result.push_back({flow, cost});
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = pv[v]) {
                c = std::min(c, g[pv[v]][pe[v]].cap);
            }
            for (int v = t; v != s; v = pv[v]) {
                auto& e = g[pv[v]][pe[v]];
                e.cap -= c;
                g[v][e.rev].cap += c;
            }
            Cost d = -dual[s];
            flow += c;
            cost += c * d;
            if (prev_cost == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost = cost;
        }
        return result;
    }
    void print() {
        for(auto e : this->edges()) {
            cout << e.from << "->" << e.to << " [" << e.flow << "/" << e.cap << "], cost = " << e.cost << endl;
        }
    }
};
int main() {
    int n,k;cin >> n >> k;
    MininumCostFlow<int,ll> g(n*2+2);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            ll a;cin >> a;a = 1000000000 - a;
            g.add_edge(i,j+n,1,a);
        }
        g.add_edge(n*2,i,k,0);
        g.add_edge(i+n,n*2+1,k,0);
    }
    g.add_edge(n*2,n*2+1,n*k,1000000000);
    auto v = g.flow(n*2,n*2+1,n*k);
    cout << (ll)v.first * 1000000000 - v.second << endl;
    vector<vector<char>> ans(n,vector<char>(n,'.'));
    for(auto e : g.edges()) {
        if (e.from == n*2 || e.to == n*2+1) continue;
        if (e.flow != 0) ans[e.from][e.to-n] = 'X';
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cout << ans[i][j];
        }
        cout << endl;
    }
    return 0;
}