Solution

solution 1:

#include "bits/stdc++.h"
using namespace std;

void setIO(string s) {
	ios_base::sync_with_stdio(0); cin.tie(0); 
	freopen((s+".in").c_str(),"r",stdin);
	freopen((s+".out").c_str(),"w",stdout);
}
 
int N;
bool G[300][300],GG[300][300];
long long ans;
 
void rot() { 
	for (int i = 0; i < N; ++i) 
		for (int j = 0; j < N; ++j) 
			GG[N-1-j][i] = G[i][j];
	for (int i = 0; i < N; ++i) 
		for (int j = 0; j < N; ++j) 
			G[i][j] = GG[i][j];
}
void solve() { 
	for (int a = 0; a < 2*N-1; ++a) 
		for (int b = a+2; b < 2*N-1; b += 2) {
			int dif = (b-a)/2, st = max(0,a-(N-1)), en = min(a,N-1);
			int cur = 0;
			for (int i = st; i <= en; ++i) { 
				if (i == st) 
					for (int j = max(i,b-(N-1)); j < min(i+dif,N-dif); ++j) 
						cur += G[j][b-j] && G[j+dif][b-j-dif];
				if (G[i][a-i]) ans += cur;
				if (i+2*dif < N && b-(i+dif) < N) 
					cur += G[i+dif][b-i-dif] && G[i+2*dif][b-i-2*dif];
				if (i+dif < N && b-i < N) 
					cur -= G[i][b-i] && G[i+dif][b-i-dif];
			}
		}
}
int main() {
	//setIO("triangles"); 
	cin >> N;
	for (int i = 0; i < N; ++i) 
		for (int j = 0; j < N; ++j) {
			char c; cin >> c;
			G[i][j] = c == '*';
		}
	for (int i = 0; i < 4; ++i) solve(), rot(); 
	cout << ans << "\n";
}

solution 2:

#include "bits/stdc++.h"
 
using namespace std;
 
void setIO(string s) {
	ios_base::sync_with_stdio(0); cin.tie(0); 
	freopen((s+".in").c_str(),"r",stdin);
	freopen((s+".out").c_str(),"w",stdout);
}
 
int N;
bool G[300][300],GG[300][300];
long long res = 0;

void rot() {
	for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) GG[N-1-j][i] = G[i][j];
	for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) G[i][j] = GG[i][j];
}

void solve() {
	bitset<300> mask[300];
	for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) 
		mask[i][j] = G[i][j];
	for (int i = 0; i < N; ++i)
		for (int x = 1; x < N; ++x) 
			for (int y = x; y < N; y += 2) {
				int x2 = x+(x+y)/2; if (i+x2 >= N) break;
				int y2 = (y-x)/2;
				res += (mask[i]&(mask[i+x]>>y)&(mask[i+x2]>>y2)).count();
			}
}

int main() {
	//setIO("triangles"); 
	cin >> N;
	for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) {
		char c; cin >> c;
		G[i][j] = c == '*';
	}
	for (int i = 0; i < 4; ++i) { solve(); rot(); }
	cout << res << "\n";
}