Problem: One fine day Sasha went to the park for a walk. In the park, he saw that his favorite bench is occupied, and he had to sit down on the neighboring one. He sat down and began to listen to the silence. Suddenly, he got a question: what if in different parts of the park, the silence sounds in different ways? So it was. Let's divide the park into 1 × 1 meter squares and call them cells, and numerate rows from 1 to n from up to down, and columns from 1 to m from left to right. And now, every cell can be described with a pair of two integers (x, y), where x — the number of the row, and y — the number of the column. Sasha knows that the level of silence in the cell (i, j) equals to f_{i,j}, and all f_{i,j} form a permutation of numbers from 1 to n ⋅ m. Sasha decided to count, how many are there pleasant segments of silence?

Let's take some segment [l … r]. Denote S as the set of cells (i, j) that l ≤ f_{i,j} ≤ r. Then, the segment of silence [l … r] is pleasant if there is only one simple path between every pair of cells from S (path can't contain cells, which are not in S). In other words, set S should look like a tree on a plain. Sasha has done this task pretty quickly, and called the algorithm — "algorithm of silence's sounds".

Time passed, and the only thing left from the algorithm is a legend. To prove the truthfulness of this story, you have to help Sasha and to find the number of different pleasant segments of silence. Two segments [l_1 … r_1], [l_2 … r_2] are different, if l_1 ≠ l_2 or r_1 ≠ r_2 or both at the same time.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 1000, 1 ≤ n ⋅ m ≤ 2 ⋅ 10^5) — the size of the park.

Each from next n lines contains m integers f_{i,j} (1 ≤ f_{i,j} ≤ n ⋅ m) — the level of silence in the cell with number (i, j).

It is guaranteed, that all f_{i,j} are different.

Output

Print one integer — the number of pleasant segments of silence.

Examples

Input

1 5
1 2 3 4 5


Output

15

Input

2 3
1 2 3
4 5 6


Output

15

Input

4 4
4 3 2 16
1 13 14 15
5 7 8 12
6 11 9 10


Output

50

Note

In the first example, all segments of silence are pleasant.

In the second example, pleasant segments of silence are the following:

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Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
 
public class Main {
 
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        TaskD solver = new TaskD(in, out);
        solver.solve();
        out.close();
    }
 
    static class TaskD {
        static private final int[] dx = {1, -1, 0, 0};
        static private final int[] dy = {0, 0, 1, -1};
 
        static int n, m;
        static int total;
 
        static int[][] f;
        static int[] posX;
        static int[] posY;
        static int[] leftBound;
 
        List<Integer>[] edges;
        LinkCutTree lct;
        InputReader in;
        OutputWriter out;
 
        TaskD(InputReader in, OutputWriter out) {
            this.in = in;
            this.out = out;
        }
 
        private void solve() {
            n = in.readInt();
            m = in.readInt();
            total = n * m;
            f = new int[n][m];
            posX = new int[total];
            posY = new int[total];
            for(int i = 0; i < n; ++i) {
                for(int j = 0; j < m; ++j) {
                    f[i][j] = in.readInt() - 1;
                    posX[f[i][j]] = i;
                    posY[f[i][j]] = j;
                }
            }
            edges = new ArrayList[total];
            leftBound = new int[total];
            lct = new LinkCutTree(total);
            for(int i = 0; i < total; ++i) {
                edges[i] = new ArrayList<>();
            }
            for(int l = 0, r = 0; r < total; ++r) {
               l = addCell(l, r);
               leftBound[r] = l;
            }
            long ans = 0;
            SegmentTree t = new SegmentTree(total + 4);
            for(int r = 0; r < total; ++r) {
                int x = posX[r];
                int y = posY[r];
                List<Integer> seg = new ArrayList<>();
                for(int i = 0; i < 4; ++i) {
                    int px = x + dx[i];
                    int py = y + dy[i];
                    if (px < 0 || px >= n) continue;
                    if (py < 0 || py >= m) continue;
                    int to = f[px][py];
                    if (to > r) continue;
                    seg.add(to);
                }
                seg.add(-1);
                seg.add(r);
                Collections.sort(seg);
                for(int i = seg.size() - 1, comp = 1; i > 0; --i) {
                    if (seg.get(i - 1) + 1 > seg.get(i)) {
                        --comp;
                        continue;
                    }
                    t.inc(seg.get(i - 1) + 1, seg.get(i) + 1, comp);
                    --comp;
                }
                ans += t.query(leftBound[r], r + 1);
            }
            out.print(ans);
        }
 
        private int addCell(int l, int r) {
            int x = posX[r];
            int y = posY[r];
            for(int i = 0; i < 4; ++i) {
                int px = x + dx[i];
                int py = y + dy[i];
                if (px < 0 || px >= n) continue;
                if (py < 0 || py >= m) continue;
                int to = f[px][py];
                while (l <= to && to <= r) {
                    if (lct.link(to, r)) {
                        edges[to].add(r);
                        break;
                    }
                    removeCell(l);
                    ++l;
                }
            }
            return l;
        }
 
        private void removeCell(int c) {
            for(int to : edges[c]) {
                lct.cut(c, to);
            }
            edges[c].clear();
        }
    }
 
    static class SegmentTree {
        int size;
        int height;
        int[] t;
        int[] cnt;
        int[] push;
 
        SegmentTree(int n) {
            this.size = n;
            this.height = 0;
            int temp = n;
            while (temp > 0) {
                temp >>= 1;
                ++this.height;
            }
            t = new int[n << 1];
            cnt = new int[n << 1];
            push = new int[n];
            for(int i = 0; i < n; ++i) {
                cnt[i + n] = 1;
            }
            for(int i = n - 1; i >= 0; --i) {
                cnt[i] = cnt[i << 1] + cnt[i << 1 | 1];
            }
        }
 
        private void apply(int p, int value) {
            t[p] += value;
            if (p < size) push[p] += value;
        }
 
        private void recalc(int p) {
            while (p > 1) {
                p >>= 1;
                t[p] = Math.min(t[p << 1], t[p << 1 | 1]) + push[p];
                cnt[p] = (t[p] == t[p << 1] + push[p] ? cnt[p << 1] : 0)
                        + (t[p] == t[p << 1 | 1] + push[p] ? cnt[p << 1 | 1] : 0);
            }
        }
 
        private void push(int p) {
            for (int s = height; s > 0; s--) {
                int i = p >> s;
                if (push[i] != 0) {
                    apply(i << 1, push[i]);
                    apply(i << 1 | 1, push[i]);
                    push[i] = 0;
                }
            }
        }
 
        private void inc(int l, int r, int value) {
            l += size;
            r += size;
            int l0 = l;
            int r0 = r;
            for (; l < r; l >>= 1, r >>= 1) {
                if ((l & 1) != 0) apply(l++, value);
                if ((r & 1) != 0) apply(--r, value);
            }
            recalc(l0);
            recalc(r0 - 1);
        }
 
        private int query(int l, int r) {
            l += size;
            r += size;
            push(l);
            push(r - 1);
            int min = Integer.MAX_VALUE;
            int minCount = 0;
            for (; l < r; l >>= 1, r >>= 1) {
                if ((l & 1) != 0) {
                    if (min > t[l]) {
                        min = t[l];
                        minCount = cnt[l];
                    } else if (min == t[l]) {
                        minCount += cnt[l];
                    }
                    ++l;
                }
                if ((r & 1) != 0) {
                    --r;
                    if (min > t[r]) {
                        min = t[r];
                        minCount = cnt[r];
                    } else if (min == t[r]) {
                        minCount += cnt[r];
                    }
                }
            }
            return minCount;
        }
    }
 
    static class LinkCutTree {
 
        private static class Node {
            Node left;
            Node right;
            Node parent;
            boolean revert;
 
            boolean isRoot() {
                return parent == null || (parent.left != this && parent.right != this);
            }
 
            void push() {
                if (revert) {
                    revert = false;
                    Node t = left;
                    left = right;
                    right = t;
                    if (left != null)   left.revert = !left.revert;
                    if (right != null)  right.revert = !right.revert;
                }
            }
        }
 
        static int size;
        Node[] nodes;
 
        LinkCutTree(int n) {
            LinkCutTree.size = n;
            nodes = new Node[n];
            for(int i = 0; i < n; ++i) {
                nodes[i] = new Node();
            }
        }
 
        private boolean link(int x, int y) {
            return link(nodes[x], nodes[y]);
        }
 
        private void cut(int x, int y) {
            cut(nodes[x], nodes[y]);
        }
 
        private static boolean link(Node x, Node y) {
            if (connected(x, y))
                return false;
            makeRoot(x);
            x.parent = y;
            return true;
        }
 
        private static void cut(Node x, Node y) {
            makeRoot(x);
            expose(y);
            if (y.right != x || x.left != null || x.right != null) {
                throw new RuntimeException("error: no edge (x,y)");
            }
            y.right.parent = null;
            y.right = null;
        }
 
        static void connect(Node ch, Node p, Boolean isLeftChild) {
            if (ch != null)
                ch.parent = p;
            if (isLeftChild != null) {
                if (isLeftChild)
                    p.left = ch;
                else
                    p.right = ch;
            }
        }
 
        static void rotate(Node x) {
            Node p = x.parent;
            Node g = p.parent;
            boolean isRootP = p.isRoot();
            boolean leftChildX = (x == p.left);
            connect(leftChildX ? x.right : x.left, p, leftChildX);
            connect(p, x, !leftChildX);
            connect(x, g, !isRootP ? p == g.left : null);
        }
 
        static void splay(Node x) {
            while (!x.isRoot()) {
                Node p = x.parent;
                Node g = p.parent;
                if (!p.isRoot())
                    g.push();
                p.push();
                x.push();
                if (!p.isRoot())
                    rotate((x == p.left) == (p == g.left) ? p/*zig-zig*/ : x/*zig-zag*/);
                rotate(x);
            }
            x.push();
        }
 
        // makes node x the root of the virtual tree, and also x becomes the leftmost node in its splay tree
        static Node expose(Node x) {
            Node last = null;
            for (Node y = x; y != null; y = y.parent) {
                splay(y);
                y.left = last;
                last = y;
            }
            splay(x);
            return last;
        }
 
        private static void makeRoot(Node x) {
            expose(x);
            x.revert = !x.revert;
        }
 
        private static boolean connected(Node x, Node y) {
            if (x == y)
                return true;
            expose(x);
            expose(y);
            return x.parent != null;
        }
    }
 
    static class OutputWriter {
        private final PrintWriter writer;
 
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
 
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
 
        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
            writer.println();
        }
 
        public void close() {
            writer.close();
        }
 
    }
 
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
 
        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }
 
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public double readDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, readInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, readInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
 
    }
}