You are given an H \times W grid. The square at the top-left corner will be represented by (0, 0), and the square at the bottom-right corner will be represented by (H-1, W-1).

Of those squares, N squares (x_1, y_1), (x_2, y_2), ..., (x_N, y_N) are painted black, and the other squares are painted white.

Let the shortest distance between white squares A and B be the minimum number of moves required to reach B from A visiting only white squares, where one can travel to an adjacent square sharing a side (up, down, left or right) in one move.

Since there are H × W - N white squares in total, there are _{(H×W-N)}C_2 ways to choose two of the white squares.

For each of these _{(H×W-N)}C_2 ways, find the shortest distance between the chosen squares, then find the sum of all those distances, modulo 1 000 000 007=10^9+7.

Constraints

* 1 \leq H, W \leq 10^6
* 1 \leq N \leq 30
* 0 \leq x_i \leq H-1
* 0 \leq y_i \leq W-1
* If i \neq j, then either x_i \neq x_j or y_i \neq y_j.
* There is at least one white square.
* For every pair of white squares A and B, it is possible to reach B from A visiting only white squares.

Input

Input is given from Standard Input in the following format:


H W
N
x_1 y_1
x_2 y_2
:
x_N y_N


Output

Print the sum of the shortest distances, modulo 10^9+7.

Examples

Input

2 3
1
1 1


Output

20


Input

2 3
1
1 2


Output

16


Input

3 3
1
1 1


Output

64


Input

4 4
4
0 1
1 1
2 1
2 2


Output

268


Input

1000000 1000000
1
0 0


Output

333211937
#include <iostream>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <cstring>
using namespace std;

#define REP(i, s) for (int i = 0; i < s; ++i)
#define ALL(v) (v.begin(), v.end())
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
#define EACH(i, s) for (__typeof__((s).begin()) i = (s).begin(); i != (s).end(); ++i)

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<class T1, class T2> ostream& operator << (ostream &s, pair<T1, T2> P)
{
	return s << '<' << P.first << ", " << P.second << '>';
}
template<class T> ostream& operator << (ostream &s, vector<T> P)
{
	for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s;
}
template<class T> ostream& operator << (ostream &s, vector<vector<T> > P)
{
	for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl;
}

const int MOD = 1000000007;
inline long long mod(long long a, long long m) { return (a % m + m) % m; }
struct Fp {
	int MOD = 1000000007;
	long long val;

	Fp() : val(0) {}
	Fp(long long val_) { this->val = mod(val_, MOD); }
	Fp operator = (long long val_) { this->val = mod(val_, MOD); return *this; }
	inline Fp operator - () { return mod(-val, MOD); }
	inline const Fp& operator += (const Fp &x);
	inline const Fp& operator -= (const Fp &x);
	inline const Fp& operator *= (const Fp &x);
	inline const Fp& operator /= (const Fp &x);
};

inline bool operator == (Fp x, Fp y) { return x.val == y.val; }
inline bool operator != (Fp x, Fp y) { return !(x == y); }

ostream &operator << (ostream &os, Fp x) { return os << x.val; }
istream &operator >> (istream &is, Fp &x) { is >> x; return is; }

inline Fp operator + (Fp x, Fp y) { return mod(x.val + y.val, x.MOD); }
inline Fp operator - (Fp x, Fp y) { return mod(x.val - y.val, x.MOD); }
inline Fp operator * (Fp x, Fp y) { return mod(x.val * y.val, x.MOD); }
inline Fp operator / (Fp x, Fp y) {
	long long a = y.val, b = x.MOD, u = 1, v = 0;
	while (b) {
		long long t = a / b;
		a -= t*b; swap(a, b);
		u -= t*v; swap(u, v);
	}
	return x * u;
}
inline Fp abs(Fp a) { return a; }
inline Fp fpow(Fp a, long long n) {
	if (n == 0) return Fp(1);
	Fp t = fpow(a, n / 2);
	t = t * t; if (n & 1) t = t * a;
	return t;
}
inline const Fp& Fp::operator += (const Fp &x) { *this = *this + x; return *this; }
inline const Fp& Fp::operator -= (const Fp &x) { *this = *this - x; return *this; }
inline const Fp& Fp::operator *= (const Fp &x) { *this = *this * x; return *this; }
inline const Fp& Fp::operator /= (const Fp &x) { *this = *this / x; return *this; }

// calc comb (small n, r ver)
const int FACT_MAX = 210000;
static Fp fp_fact_val[FACT_MAX];

void calcFact(int MAX = FACT_MAX) {
	fp_fact_val[0] = 1;
	for (int val = 1; val < MAX; ++val) {
		fp_fact_val[val] = fp_fact_val[val - 1] * val;
	}
}

Fp fact(int n) {
	return fp_fact_val[n];
}

Fp com(int n, int r) {
	return fact(n) / fact(r) / fact(n - r);
}

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

long long H, W, N;
long long bx[210], by[210];
vector<long long> altx, alty;
long long nH, nW;

long long xnum[1100000], ynum[1100000];

bool cb[210][210];
long long dist[210][210];

typedef pair<int, int> pint;

long long subsolve() {
	//COUT(nH); COUT(nW); COUT(altx); COUT(alty);

	for (int x = 0; x < nH - 1; ++x) {
		for (int y = 0; y < nW - 1; ++y) {
			//cout << cb[x][y];
		}
		//cout << endl;
	}

  long long res = 0;
	for (int x = 0; x < nH - 1; ++x) {
		for (int y = 0; y < nW - 1; ++y) {
			if (cb[x][y]) continue;
			memset(dist, -1, sizeof(dist));
			queue<pint> que;
			que.push(pint(x, y));
			dist[x][y] = 0;
			while (!que.empty()) {
				pint cur = que.front();
				que.pop();
				for (int dir = 0; dir < 4; ++dir) {
					int nx = cur.first + dx[dir];
					int ny = cur.second + dy[dir];
					if (nx < 0 || nx >= nH-1 || ny < 0 || ny >= nW-1) continue;
					if (cb[nx][ny]) continue;
					if (dist[nx][ny] == -1) {
						dist[nx][ny] = dist[cur.first][cur.second] + 1;
						que.push(pint(nx, ny));
					}
				}
			}
			
			for (int nx = 0; nx < nH - 1; ++nx) {
				for (int ny = 0; ny < nW - 1; ++ny) {
					if (nW * nx + ny <= nW * x + y) continue;
					if (dist[nx][ny] == -1) continue;
					if (cb[nx][ny]) continue;

					long long ss = ((long long)(altx[x + 1] - altx[x]) * (alty[y + 1] - alty[y])) % MOD;
					long long st = ((long long)(altx[nx + 1] - altx[nx]) * (alty[ny + 1] - alty[ny])) % MOD;
					res += (dist[nx][ny] % MOD) * ss % MOD * st % MOD;
					res %= MOD;

					//cout << pint(x, y) << ", " << pint(nx, ny) << ": " << dist[nx][ny] << ", " << ss << ", " << st << endl;
				}
			}
			
		}
	}
	//COUT(res);
	//res /= 2;

	return res;
}

Fp solve() {
  memset(xnum, 0, sizeof(xnum));
  memset(ynum, 0, sizeof(ynum));
	altx.clear();
	alty.clear();
  altx.push_back(0);
  altx.push_back(H);
  alty.push_back(0);
  alty.push_back(W);
  for (int i = 0; i < N; ++i) {
		altx.push_back(bx[i]);
		altx.push_back(bx[i] + 1);
		alty.push_back(by[i]);
		alty.push_back(by[i] + 1);
		xnum[bx[i]]++;
		ynum[by[i]]++;
  }
  sort(altx.begin(), altx.end());
  sort(alty.begin(), alty.end());
  altx.erase(unique(altx.begin(), altx.end()), altx.end());
  alty.erase(unique(alty.begin(), alty.end()), alty.end());
  nH = altx.size();
  nW = alty.size();

  memset(cb, 0, sizeof(cb));
  for (int i = 0; i < N; ++i) {
		int itx = lower_bound(altx.begin(), altx.end(), bx[i]) - altx.begin();
		int ity = lower_bound(alty.begin(), alty.end(), by[i]) - alty.begin();
		cb[itx][ity] = true;
  }

  long long all = (long long)H * W - N;
  Fp add = 0;
  long long width = W;
	long long num_comped = 0;
  long long sum = width - xnum[0];
  for (int i = 1; i < H; ++i) {
		if (xnum[i] == 0 && xnum[i-1] == 0) {   // i-1 -> i
			Fp up = sum - width * num_comped;
			Fp down = all - sum;
			add += up * down;
		}
		sum += width - xnum[i];
  }
  long long height = H - num_comped;
  all -= width * num_comped;
  num_comped = 0;
  sum = height - ynum[0];
  for (int i = 1; i < W; ++i) {
		if (ynum[i] == 0 && ynum[i-1] == 0) {   // i-1 -> i
			Fp left = sum - height * num_comped;
			Fp right = all - sum;
			add += left * right;
		}
		sum += height - ynum[i];
  }

  Fp comp = subsolve();
  Fp res = comp + add;

	//COUT(add);

  return res;
}

int main() {
  while (cin >> H >> W >> N) {
		for (int i = 0; i < N; ++i) cin >> bx[i] >> by[i];
		cout << solve() << endl;
  }
}
