You are wandering in the explorer space of the 2050 Conference.

The explorer space can be viewed as an undirected weighted grid graph with size n× m. The set of vertices is \{(i, j)|1≤ i≤ n, 1≤ j≤ m\}. Two vertices (i_1,j_1) and (i_2, j_2) are connected by an edge if and only if |i_1-i_2|+|j_1-j_2|=1.

At each step, you can walk to any vertex connected by an edge with your current vertex. On each edge, there are some number of exhibits. Since you already know all the exhibits, whenever you go through an edge containing x exhibits, your boredness increases by x.

For each starting vertex (i, j), please answer the following question: What is the minimum possible boredness if you walk from (i, j) and go back to it after exactly k steps?

You can use any edge for multiple times but the boredness on those edges are also counted for multiple times. At each step, you cannot stay on your current vertex. You also cannot change direction while going through an edge. Before going back to your starting vertex (i, j) after k steps, you can visit (i, j) (or not) freely.

Input

The first line contains three integers n, m and k (2≤ n, m≤ 500, 1≤ k≤ 20).

The j-th number (1≤ j ≤ m - 1) in the i-th line of the following n lines is the number of exibits on the edge between vertex (i, j) and vertex (i, j+1). 

The j-th number (1≤ j≤ m) in the i-th line of the following n-1 lines is the number of exibits on the edge between vertex (i, j) and vertex (i+1, j). 

The number of exhibits on each edge is an integer between 1 and 10^6.

Output

Output n lines with m numbers each. The j-th number in the i-th line, answer_{ij}, should be the minimum possible boredness if you walk from (i, j) and go back to it after exactly k steps.

If you cannot go back to vertex (i, j) after exactly k steps, answer_{ij} should be -1. 

Examples

Input


3 3 10
1 1
1 1
1 1
1 1 1
1 1 1


Output


10 10 10
10 10 10
10 10 10


Input


2 2 4
1
3
4 2


Output


4 4
10 6


Input


2 2 3
1
2
3 4


Output


-1 -1
-1 -1

Note

In the first example, the answer is always 10 no matter how you walk.

In the second example, answer_{21} = 10, the path is (2,1) → (1,1) → (1,2) → (2,2) → (2,1), the boredness is 4 + 1 + 2 + 3 = 10.


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;

public class P1517D {
	// author: Nagabhushan S Baddi

	// PRIMARY VARIABLES
	private static int n, m, k;
	private static int[][] hor, ver, a, b;
	private static long ans;
	private static int[][] id;
	private static Integer[][][] dp;
	private static int idf;
	private static String s, t;
	private static HashMap<Integer, ArrayList<Integer>> g;

	// CONSTANTS
	private static final int MOD = (int) 1e9 + 7;

	public static void main(String[] args) {
		n = ini();
		m = ini();
		k = ini();
		
		if (k%2!=0) {
			for(int i=0; i<n; i++) {
				for(int j=0; j<m; j++) {
					print(-1+" ");
				}
				println();
			}
			out.flush();
			return;
		}

		hor = new int[n][m-1];
		ver = new int[n-1][m];
		
		for(int i=0; i<n; i++) {
			for(int j=0; j<m-1; j++) {
				hor[i][j] = ini();
			}
		}
		for(int i=0; i<n-1; i++) {
			for(int j=0; j<m; j++) {
				ver[i][j] = ini();
			}
		}
		
		dp = new Integer[n][m][k+1];
		
		for(int i=0; i<n; i++) {
			for(int j=0; j<m; j++) {
				print(2*solve(i, j, k/2)+" ");
			}
			println();
		}
		
		out.flush();
		out.close();

	}
	
	private static int solve(int i, int j, int kLeft) {
		if (i<0 || i>=n || j<0 || j>=m) {
			return (int)1e9;
		} else if (kLeft==0) {
			return 0;
		}
		
		if (dp[i][j][kLeft]!=null) {
			return dp[i][j][kLeft];
		}
		
		int ans = (int)1e9;
		
		final int[] dx = {-1, 1, 0, 0};
		final int[] dy = {0, 0, -1, 1};
		
		for(int type=0; type<4; type++) {
			int ni = i+dx[type];
			int nj = j+dy[type];
			if (ni<0 || ni>=n || nj<0 || nj>=m) continue;
			
			int inhibit = 0;
			if (type==0) {
				inhibit = ver[ni][nj];
			} else if (type==1) {
				inhibit = ver[i][j];
			} else if (type==2) {
				inhibit = hor[ni][nj];
			} else {
				inhibit = hor[i][j];
			}
			
			ans = Math.min(ans, inhibit+solve(ni, nj, kLeft-1));
		}
		
		return dp[i][j][kLeft]=ans;
	}

	// INIT
	private static void initCase(int z) {
		idf = z;
		ans = 0;
	}

	// PRINT ANSWER
	private static void printAns(Object o) {
		out.println(o);
	}

	private static void printAns(Object o, int testCaseNo) {
		out.println("Case #" + testCaseNo + ": " + o);
	}

	private static void printArray(Object[] a) {
		for (int i = 0; i < a.length; i++) {
			out.print(a[i] + " ");
		}
		out.println();
	}

	// SORT SHORTCUTS - QUICK SORT TO MERGE SORT
	private static void sort(int[] a) {
		int n = a.length;
		Integer[] b = new Integer[n];
		for (int i = 0; i < n; i++) {
			b[i] = a[i];
		}

		Arrays.sort(b);

		for (int i = 0; i < n; i++) {
			a[i] = b[i];
		}
	}

	private static void sort(long[] a) {
		int n = a.length;
		Long[] b = new Long[n];
		for (int i = 0; i < n; i++) {
			b[i] = a[i];
		}

		Arrays.sort(b);

		for (int i = 0; i < n; i++) {
			a[i] = b[i];
		}
	}

	// INPUT SHORTCUTS

	private static int[] ina(int n) {
		int[] temp = new int[n];
		for (int i = 0; i < n; i++) {
			temp[i] = in.nextInt();
		}
		return temp;
	}

	private static int[][] ina2d(int n, int m) {
		int[][] temp = new int[n][m];
		for (int i = 0; i < n; i++) {
			temp[i] = ina(m);
		}
		return temp;
	}

	private static int ini() {
		return in.nextInt();
	}

	private static long inl() {
		return in.nextLong();
	}

	private static double ind() {
		return Double.parseDouble(ins());
	}

	private static String ins() {
		return in.readString();
	}

	// PRINT SHORTCUTS
	private static void println(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
		out.write("\n");
	}

	private static void pd(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
		out.flush();
		out.write("\n");
	}

	private static void print(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
	}

	// GRAPH SHORTCUTS
	private static HashMap<Integer, ArrayList<Integer>> intree(int n) {

		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();
		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < n - 1; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
			g.get(v).add(u);
		}

		return g;
	}

	private static HashMap<Integer, ArrayList<Integer>> ingraph(int n, int m) {
		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();

		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
			g.get(v).add(u);
		}

		return g;

	}

	private static HashMap<Integer, ArrayList<Integer>> indirectedgraph(int n, int m) {
		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();

		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
		}

		return g;

	}

	private static HashMap<Integer, ArrayList<Edge>> inweightedgraph(int n, int m) {
		HashMap<Integer, ArrayList<Edge>> g = new HashMap<>();

		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			int w = ini();
			Edge edge = new Edge(u, v, w);
			g.get(u).add(edge);
			g.get(v).add(edge);
		}

		return g;

	}

	private static class Edge implements Comparable<Edge> {
		private int u, v;
		private long w;

		public Edge(int a, int b, long c) {
			u = a;
			v = b;
			w = c;
		}

		public int other(int x) {
			return (x == u ? v : u);
		}

		public int compareTo(Edge edge) {
			return Long.compare(w, edge.w);
		}
	}

	private static class Pair {
		private int u, v;

		public Pair(int a, int b) {
			u = a;
			v = b;
		}

		public int hashCode() {
			return u + v + u * v;
		}

		public boolean equals(Object object) {
			Pair pair = (Pair) object;
			return u == pair.u && v == pair.v;
		}
	}

	private static class Node implements Comparable<Node> {
		private int u;
		private long dist;

		public Node(int a, long b) {
			u = a;
			dist = b;
		}

		public int compareTo(Node node) {
			return Long.compare(dist, node.dist);
		}
	}

	// MATHS AND NUMBER THEORY SHORTCUTS
	private static int gcd(int a, int b) {
		// O(log(min(a,b)))
		if (b == 0)
			return a;

		return gcd(b, a % b);
	}

	private static long modExp(long a, long b) {
		if (b == 0)
			return 1;

		a %= MOD;

		long exp = modExp(a, b / 2);

		if (b % 2 == 0) {
			return (exp * exp) % MOD;
		} else {
			return (a * ((exp * exp) % MOD)) % MOD;
		}
	}

	private long mul(int a, int b) {
		return a * 1L * b;
	}

	// Segment Tree
	private static class SegmentTree<T extends Comparable<T>> {
		private int n, m;
		private T[] a;
		private T[] seg;
		private T NULLVALUE;

		public SegmentTree(int n, T NULLVALUE) {
			this.NULLVALUE = NULLVALUE;
			this.n = n;
			m = 4 * n;
			seg = (T[]) new Object[m];

		}

		public SegmentTree(T[] a, int n, T NULLVALUE) {
			this.NULLVALUE = NULLVALUE;
			this.a = a;
			this.n = n;
			m = 4 * n;
			seg = (T[]) new Object[m];
			construct(0, n - 1, 0);
		}

		private void update(int pos) {
			// Range Sum
			// seg[pos] = seg[2*pos+1]+seg[2*pos+2];

			// Range Min
			if (seg[2 * pos + 1].compareTo(seg[2 * pos + 2]) <= 0) {
				seg[pos] = seg[2 * pos + 1];
			} else {
				seg[pos] = seg[2 * pos + 2];
			}
		}

		private T optimum(T leftValue, T rightValue) {
			// Range Sum
			// return leftValue+rightValue;

			// Range Min
			if (leftValue.compareTo(rightValue) <= 0) {
				return leftValue;
			} else {
				return rightValue;
			}
		}

		public void construct(int low, int high, int pos) {
			if (low == high) {
				seg[pos] = a[low];
				return;
			}

			int mid = (low + high) / 2;

			construct(low, mid, 2 * pos + 1);
			construct(mid + 1, high, 2 * pos + 2);
			update(pos);
		}

		public void add(int index, T value) {
			add(index, value, 0, n - 1, 0);
		}

		private void add(int index, T value, int low, int high, int pos) {
			if (low == high) {
				seg[pos] = value;
				return;
			}

			int mid = (low + high) / 2;

			if (index <= mid) {
				add(index, value, low, mid, 2 * pos + 1);
			} else {
				add(index, value, mid + 1, high, 2 * pos + 2);
			}
			update(pos);
		}

		public T get(int qlow, int qhigh) {
			return get(qlow, qhigh, 0, n - 1, 0);
		}

		public T get(int qlow, int qhigh, int low, int high, int pos) {
			if (qlow > low || low > qhigh) {
				return NULLVALUE;
			} else if (qlow <= low || qhigh >= high) {
				return seg[pos];
			} else {
				int mid = (low + high) / 2;
				T leftValue = get(qlow, qhigh, low, mid, 2 * pos + 1);
				T rightValue = get(qlow, qhigh, mid + 1, high, 2 * pos + 2);

				return optimum(leftValue, rightValue);
			}
		}
	}

	// DSU
	private static class DSU {
		private int[] id;
		private int[] size;
		private int n;

		public DSU(int n) {
			this.n = n;

			id = new int[n];
			for (int i = 0; i < n; i++) {
				id[i] = i;
			}

			size = new int[n];
			Arrays.fill(size, 1);
		}

		private int root(int u) {
			while (u != id[u]) {
				id[u] = id[id[u]];
				u = id[u];
			}
			return u;
		}

		public boolean connected(int u, int v) {
			return root(u) == root(v);
		}

		public void union(int u, int v) {
			int p = root(u);
			int q = root(v);

			if (size[p] >= size[q]) {
				id[q] = p;
				size[p] += size[q];
			} else {
				id[p] = q;
				size[q] += size[p];
			}
		}
	}

	// KMP
	private static int countSearch(String s, String p) {
		int n = s.length();
		int m = p.length();

		int[] b = backTable(p);

		int j = 0;
		int count = 0;

		for (int i = 0; i < n; i++) {
			if (j == m) {
				j = b[j - 1];
				count++;
			}
			while (j != 0 && s.charAt(i) != p.charAt(j)) {
				j = b[j - 1];
			}
			if (s.charAt(i) == p.charAt(j)) {
				j++;
			}
		}

		if (j == m)
			count++;

		return count;
	}

	private static int[] backTable(String p) {
		int m = p.length();

		int j = 0;
		int[] b = new int[m];

		for (int i = 1; i < m; i++) {
			while (j != 0 && p.charAt(i) != p.charAt(j)) {
				j = b[j - 1];
			}
			if (p.charAt(i) == p.charAt(j)) {
				b[i] = ++j;
			}
		}
		return b;
	}

	private static class LCA {
		private HashMap<Integer, ArrayList<Integer>> g;
		private int[] level;
		private int[] a;
		private int[][] P;
		private int n, m;
		private int[] xor;

		public LCA(HashMap<Integer, ArrayList<Integer>> g, int[] a) {
			this.g = g;
			this.a = a;
			n = g.size();
			m = (int) (Math.log(n) / Math.log(2)) + 5;
			P = new int[n][m];
			xor = new int[n];
			level = new int[n];

			preprocess();
		}

		private void preprocess() {
			dfs(0, -1);

			for (int j = 1; j < m; j++) {
				for (int i = 0; i < n; i++) {
					if (P[i][j - 1] != -1) {
						P[i][j] = P[P[i][j - 1]][j - 1];
					}
				}
			}
		}

		private void dfs(int u, int p) {
			P[u][0] = p;
			xor[u] = a[u] ^ (p == -1 ? 0 : xor[p]);
			level[u] = (p == -1 ? 0 : level[p] + 1);

			for (int v : g.get(u)) {
				if (v == p)
					continue;
				dfs(v, u);
			}
		}

		public int lca(int u, int v) {
			if (level[v] > level[u]) {
				int temp = v;
				v = u;
				u = temp;
			}

			for (int j = m; j >= 0; j--) {
				if (level[u] - (1 << j) < level[v]) {
					continue;
				} else {
					u = P[u][j];
				}
			}

			if (u == v)
				return u;

			for (int j = m - 1; j >= 0; j--) {
				if (P[u][j] == -1 || P[u][j] == P[v][j]) {
					continue;
				} else {
					u = P[u][j];
					v = P[v][j];
				}
			}

			return P[u][0];
		}

		private int xor(int u, int v) {
			int l = lca(u, v);

			return xor[u] ^ xor[v] ^ a[l];
		}
	}

	// FAST INPUT OUTPUT LIBRARY
	private static InputReader in = new InputReader(System.in);
	private static PrintWriter out = new PrintWriter(System.out);

	private static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;

		public InputReader(InputStream st) {
			this.stream = st;
		}

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}
}


