#include <bits/stdc++.h>
#include "rect.h"
using namespace std;
typedef pair<int,int> pii;
const int LOG = 12;
const int MAXN = 2510;
const int INF = 1000000010;
const int MAXS = 2500*2500 + 10;
struct query
{
int L, R;
int ind, k;
query(int l, int r, int i, int k)
: L(l), R(r), ind(i), k(k) {}
};
class RMQ
{
public:
int cmp(int a, int b, int t)
{
if( t == 0 ) return max( a , b );
return min( a, b );
}
void build(vector<int>& v, int t)
{
int n = (int)v.size();
for(int i = 1 ; i <= n ; i++)
tab[0][i] = v[i - 1];
for(int k = 0 ; k < LOG - 1 ; k++)
for(int L = 1 ; L + (1 << (k + 1)) <= n + 1 ; L++)
tab[k + 1][L] = cmp( tab[k][L] , tab[k][L + (1 << k)] , t );
}
int query(int L, int R, int t)
{
int sz = R - L + 1;
int k = 31 - __builtin_clz(sz);
return cmp( tab[k][L] , tab[k][R + 1 - (1 << k)] , t );
}
private:
int tab[LOG][MAXN];
};
int n, m;
int v[MAXN][MAXN], qtd[MAXS];
int L[MAXN][MAXN], U[MAXN][MAXN];
int R[MAXN][MAXN][2], D[MAXN][MAXN][2];
vector<query> lineMin[MAXN], columnMin[MAXN];
vector<query> lineMax[MAXN], columnMax[MAXN];
RMQ curRMQ;
void makeHistogram()
{
for(int i = 1 ; i <= n ; i++)
{
for(int j = 1 ; j <= m ; j++)
{
int& ansL = L[i][j]; ansL = j - 1;
int& ansU = U[i][j]; ansU = i - 1;
while( v[i][ansL] < v[i][j] ) ansL = L[i][ansL];
while( v[ansU][j] < v[i][j] ) ansU = U[ansU][j];
}
}
for(int j = m ; j > 0 ; j--)
{
for(int i = n ; i > 0 ; i--)
{
int ansR[2] = { j + 1 , j + 1 };
int ansD[2] = { i + 1 , i + 1 };
while( v[i][ ansR[1] ] < v[i][j] ) ansR[1] = R[i][ ansR[1] ][1];
while( v[i][ ansR[0] ] <= v[i][j] ) ansR[0] = R[i][ ansR[0] ][0];
while( v[ ansD[1] ][j] < v[i][j] ) ansD[1] = D[ ansD[1] ][j][1];
while( v[ ansD[0] ][j] <= v[i][j] ) ansD[0] = D[ ansD[0] ][j][0];
R[i][j][0] = ansR[0]; R[i][j][1] = ansR[1];
D[i][j][0] = ansD[0]; D[i][j][1] = ansD[1];
}
}
}
long long count_rectangles(vector< vector<int> > a)
{
n = a.size();
m = a[0].size();
for(int i = 0 ; i <= n + 1 ; i++)
for(int j = 0 ; j <= m + 1 ; j++)
v[i][j] = INF;
for(int i = 0 ; i < n ; i++)
for(int j = 0 ; j < m ; j++)
v[i + 1][j + 1] = a[i][j];
makeHistogram();
vector< pair<pii,pii> > rect;
for(int i = 2 ; i < n ; i++)
{
for(int j = 2 ; j < m ; j++)
{
if( L[i][j] == 0 || U[i][j] == 0 ) continue;
if( R[i][j][0] == m + 1 || D[i][j][0] == n + 1 ) continue;
pii dY = { L[i][j] + 1 , R[i][j][0] - 1 };
pii dX = { U[i][j] + 1 , D[i][j][0] - 1 };
rect.push_back( { dX , dY } );
}
}
sort( rect.begin() , rect.end() );
auto it = unique( rect.begin() , rect.end() );
rect.resize( it - rect.begin() );
for(int i = 0 ; i < (int)rect.size() ; i++)
{
int x1 = rect[i].first.first;
int x2 = rect[i].first.second;
int y1 = rect[i].second.first;
int y2 = rect[i].second.second;
lineMin[y1 - 1].push_back( query( x1 , x2 , i , y2 ) );
lineMax[y2 + 1].push_back( query( x1 , x2 , i , y1 ) );
columnMin[x1 - 1].push_back( query( y1 , y2 , i , x2 ) );
columnMax[x2 + 1].push_back( query( y1 , y2 , i , y1 ) );
}
for(int i = 1 ; i <= n ; i++)
{
vector<int> curMx, curMn;
for(int j = 1 ; j <= m ; j++)
{
curMn.push_back( U[i][j] );
curMx.push_back( D[i][j][1] );
}
curRMQ.build( curMx , 0 );
while( !lineMax[i].empty() )
{
int k = lineMax[i].back().k;
int curL = lineMax[i].back().L;
int curR = lineMax[i].back().R;
int ind = lineMax[i].back().ind;
lineMax[i].pop_back();
if( curRMQ.query( curL , curR , 0 ) <= k )
qtd[ind]++;
}
curRMQ.build( curMn , 1 );
while( !lineMin[i].empty() )
{
int k = lineMin[i].back().k;
int curL = lineMin[i].back().L;
int curR = lineMin[i].back().R;
int ind = lineMin[i].back().ind;
lineMin[i].pop_back();
if( curRMQ.query( curL , curR , 1 ) >= k )
qtd[ind]++;
}
}
for(int j = 1 ; j <= m ; j++)
{
vector<int> curMx, curMn;
for(int i = 1 ; i <= n ; i++)
{
curMn.push_back( L[i][j] );
curMx.push_back( R[i][j][1] );
}
curRMQ.build( curMx , 0 );
while( !columnMax[j].empty() )
{
int k = columnMax[j].back().k;
int curL = columnMax[j].back().L;
int curR = columnMax[j].back().R;
int ind = columnMax[j].back().ind;
columnMax[j].pop_back();
if( curRMQ.query( curL , curR , 0 ) <= k )
qtd[ind]++;
}
curRMQ.build( curMn , 1 );
while( !columnMin[j].empty() )
{
int k = columnMin[j].back().k;
int curL = columnMin[j].back().L;
int curR = columnMin[j].back().R;
int ind = columnMin[j].back().ind;
columnMin[j].pop_back();
if( curRMQ.query( curL , curR , 1 ) >= k )
qtd[ind]++;
}
}
int ans = 0;
for(int i = 0 ; i < (int)rect.size() ; i++)
if( qtd[i] == 0 ) ans++;
return ans;
}
