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 CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize(3)
using namespace std;
template <typename T>
inline bool chkmin(T &x, T y) {
  return x > y ? x = y, 1 : 0;
}
template <typename T>
inline bool chkmax(T &x, T y) {
  return x < y ? x = y, 1 : 0;
}
template <typename T>
inline void read(T &x) {
  char ch = getchar();
  int f = 1;
  x = 0;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  x *= f;
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x), read(args...);
}
int n, m, a[1050][1050], st;
long long ans;
pair<int, int> pos[200050];
struct LCT {
  int fa[200050], ch[200050][2], tag[200050];
  bool nroot(int u) { return ch[fa[u]][0] == u || ch[fa[u]][1] == u; }
  bool son(int u) { return ch[fa[u]][1] == u; }
  void rotate(int x) {
    int y = fa[x], z = fa[y], k = son(x), w = ch[x][!k];
    if (nroot(y)) ch[z][son(y)] = x;
    ch[x][!k] = y, ch[y][k] = w;
    fa[w] = y, fa[y] = x, fa[x] = z;
  }
  void put_tag(int u) { tag[u] ^= 1, swap(ch[u][0], ch[u][1]); }
  void push(int u) {
    if (tag[u]) put_tag(ch[u][0]), put_tag(ch[u][1]), tag[u] = 0;
  }
  void pushall(int u) {
    if (nroot(u)) pushall(fa[u]);
    push(u);
  }
  void splay(int x) {
    pushall(x);
    while (nroot(x)) {
      int y = fa[x];
      if (nroot(y)) rotate(son(y) ^ son(x) ? x : y);
      rotate(x);
    }
  }
  void access(int x) {
    for (register int y = 0; x; x = fa[y = x]) splay(x), ch[x][1] = y;
  }
  void mroot(int u) { access(u), splay(u), put_tag(u); }
  void split(int u, int v) { mroot(u), access(v), splay(v); }
  void link(int u, int v) { split(u, v), fa[u] = v; }
  void cut(int u, int v) { split(u, v), ch[v][0] = fa[u] = 0; }
  int find(int u) {
    access(u), splay(u);
    while (ch[u][0]) push(u = ch[u][0]);
    return splay(u), u;
  }
} T;
struct node {
  int minv, cnt;
  node operator+(const int x) { return node{minv + x, cnt}; }
  node operator+(const node &x) {
    node r;
    r.minv = min(minv, x.minv);
    r.cnt = cnt * (minv == r.minv) + x.cnt * (x.minv == r.minv);
    return r;
  }
};
struct SGT {
  int tag[200050 << 2];
  node res[200050 << 2];
  void build(int u, int l, int r) {
    if (l == r) return (void)(res[u].cnt = 1);
    build(u << 1, l, ((l + r) >> 1)), build(u << 1 | 1, ((l + r) >> 1) + 1, r);
    res[u] = res[u << 1] + res[u << 1 | 1];
  }
  void put_tag(int u, int w) { tag[u] += w, res[u] = res[u] + w; }
  void push(int u) {
    if (tag[u])
      put_tag(u << 1, tag[u]), put_tag(u << 1 | 1, tag[u]), tag[u] = 0;
  }
  void modify(int u, int l, int r, int tl, int tr, int w) {
    if (tl <= l && r <= tr) return put_tag(u, w);
    push(u);
    if (tl <= ((l + r) >> 1)) modify(u << 1, l, ((l + r) >> 1), tl, tr, w);
    if (((l + r) >> 1) < tr)
      modify(u << 1 | 1, ((l + r) >> 1) + 1, r, tl, tr, w);
    res[u] = res[u << 1] + res[u << 1 | 1];
  }
  node query(int u, int l, int r, int tl, int tr) {
    if (tl <= l && r <= tr) return res[u];
    push(u);
    if (tr <= ((l + r) >> 1)) return query(u << 1, l, ((l + r) >> 1), tl, tr);
    if (((l + r) >> 1) < tl)
      return query(u << 1 | 1, ((l + r) >> 1) + 1, r, tl, tr);
    return query(u << 1, l, ((l + r) >> 1), tl, tr) +
           query(u << 1 | 1, ((l + r) >> 1) + 1, r, tl, tr);
  }
} S;
void insert(int u, int v) {
  if (v < st || v > u) return;
  while (T.find(u) == T.find(v)) {
    int x = pos[st].first, y = pos[st].second;
    if (st <= a[x + 1][y] && a[x + 1][y] < u) T.cut(st, a[x + 1][y]);
    if (st <= a[x - 1][y] && a[x - 1][y] < u) T.cut(st, a[x - 1][y]);
    if (st <= a[x][y + 1] && a[x][y + 1] < u) T.cut(st, a[x][y + 1]);
    if (st <= a[x][y - 1] && a[x][y - 1] < u) T.cut(st, a[x][y - 1]);
    ++st;
  }
  if (st <= v) T.link(u, v);
  S.modify(1, 1, n * m, 1, v, -1);
}
int main() {
  read(n, m);
  for (register int i = 1; i <= n; ++i)
    for (register int j = 1; j <= m; ++j)
      read(a[i][j]), pos[a[i][j]] = make_pair(i, j);
  S.build(1, 1, n * m);
  st = 1;
  for (register int i = 1; i <= n * m; ++i) {
    S.modify(1, 1, n * m, 1, i, 1);
    int x = pos[i].first, y = pos[i].second;
    insert(i, a[x - 1][y]), insert(i, a[x + 1][y]), insert(i, a[x][y - 1]),
        insert(i, a[x][y + 1]);
    node _r = S.query(1, 1, n * m, st, i);
    ans += _r.cnt;
  }
  cout << ans << endl;
  return 0;
}