Lunar New Year is approaching, and you bought a matrix with lots of "crosses".

This matrix M of size n × n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 ≤ i, j ≤ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) =  'X'.

The following figure illustrates a cross appearing at position (2, 2) in a 3 × 3 matrix.
    
    
      
    X.X  
    .X.  
    X.X  
    

Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.

Input

The first line contains only one positive integer n (1 ≤ n ≤ 500), denoting the size of the matrix M.

The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 ≤ i, j ≤ n.

Output

Output a single line containing only one integer number k — the number of crosses in the given matrix M.

Examples

Input


5
.....
.XXX.
.XXX.
.XXX.
.....


Output


1


Input


2
XX
XX


Output


0


Input


6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......


Output


4

Note

In the first sample, a cross appears at (3, 3), so the answer is 1.

In the second sample, no crosses appear since n < 3, so the answer is 0.

In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
	import java.util.*;
	import java.io.*;
	import java.lang.reflect.Array;
	
			public class codeforces
			{	
				public static void main(String[] args)
				{
					InputReader in = new InputReader(System.in);
					PrintWriter pw = new PrintWriter(System.out);
					
					int n = in.nextInt();
					int ans = 0;
					char[][] a = new char[n][n];
					
					for(int i=0;i<n;i++)
					{
						String s = in.nextLine();
						
						a[i] = s.toCharArray();
					}
					
					for(int i=1;i<n-1;i++)
					{
						for(int j=1;j<n-1;j++)
						{
							if(a[i][j] == a[i-1][j-1] && a[i][j] == a[i-1][j+1] && a[i][j] == a[i+1][j-1] && a[i][j] == a[i+1][j+1] && a[i][j] == 'X')
								ans++;
						}
					}
					
					pw.println(ans);
					
					pw.flush();
					pw.close();
				}
				
				public static int BinarySearch_l(long[] a, long k)
				{
					int n = a.length;
					int i = 0, j = n-1;
					int mid = 0;
					
					if(k - a[n-1] > 0)
						return n;
					else
					{
						while(j - i > 0)
						{
							mid = (i+j)/2;
							
							if(k - a[mid] > 0)
								i = mid + 1;
							else
								j = mid;
						}
					}
					
					return i;
				}
				
				public static int BinarySearch_r(long[] a, long k)
				{
					int n = a.length;
					int i = 0, j = n-1;
					int mid = 0;
					
					if(k - a[0] < 0)
						return -1;
					else
					{
						while(j - i > 0)
						{
							mid = (int)Math.ceil((double)(i+j)/2);
							
							if(k - a[mid] >= 0)
								i = mid;
							else
								j = mid - 1;
						}
					}
					
					return i;
				}
				public static long fact(long n, long M)
				{
					long ans = 1;
					
					for(long i=n;i>0;i--)
					{
						ans = (ans*i)%M;
					}
					
					return ans;
				}
				
			/*	public static void DFS(int sourse)
				{
					int count = 0;
					visited[sourse] = true;
					
					for(int u : adj[sourse])
					{
						if(!visited[u])
						{
							DFS(u);
						}
					}
					
					
				}*/
				
				public static ArrayList Divisors(int n)
				{
				    ArrayList<Integer> div = new ArrayList<>();
				    
				    for (int i=1; i<=Math.sqrt(n); i++)
				    {
				        if (n%i == 0)
				        {
				        	div.add(i);
				                
				            if(n/i != i)
				            	div.add(n/i);
				        }
				    }
				    return div;
				}
			
				public static long GCD(long a,long b)
				{
					if(b==0)
						return a;
					else
						return GCD(b,a%b);
				}
				
				public static long LCM(long a,long b)
				{
					return (a*b)/GCD(a, b);
				}
				
				static class pair implements Comparable<pair>
				{
					Integer x, y;
					pair(int x,int y)
					{
						this.x=x;
						this.y=y;
					}
					
					public int compareTo(pair o) {
						int result = x.compareTo(o.x);
						if(result==0)
							result = y.compareTo(o.y);
						
						return result;
					}  
					
					public String toString()
					{
						return x+" "+y;
					}
					
					public boolean equals(Object o)
					{
						if (o instanceof pair)
					    {
							pair p = (pair)o;
							return p.x - x == 0 && p.y - y == 0 ;
						}
						return false;
					}
					
					public int hashCode()
					{
						return new Long(x).hashCode()*31 + new Long(y).hashCode();
					}
				}
				
				static class InputReader 
				{
					 
					private final InputStream stream;
					private final byte[] buf = new byte[8192];
					private int curChar, snumChars;
					private SpaceCharFilter filter;
			 
					public InputReader(InputStream stream) 
					{
						this.stream = stream;
					}
			 
					public int snext() 
					{
						if (snumChars == -1)
							throw new InputMismatchException();
						if (curChar >= snumChars) 
						{
							curChar = 0;
							try 
							{
								snumChars = stream.read(buf);
							} 
							catch (IOException e) 
							{
								throw new InputMismatchException();
							}
							if (snumChars <= 0)
								return -1;
						}
						return buf[curChar++];
					}
			 
					public int nextInt() 
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						int sgn = 1;
						if (c == '-')
					    {
							sgn = -1;
							c = snext();
						}
						int res = 0;
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
			 
					public long nextLong()
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						int sgn = 1;
						if (c == '-') 
						{
							sgn = -1;
							c = snext();
						}
						long res = 0;
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
			 
					public int[] nextIntArray(int n) 
					{
						int a[] = new int[n];
						for (int i = 0; i < n; i++) 
						{
							a[i] = nextInt();
						}
						return a;
					}
			 
					public String readString()
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = snext();
						} while (!isSpaceChar(c));
						return res.toString();
					}
			 
					public String nextLine() 
					{
						int c = snext();
						while (isSpaceChar(c))
							c = snext();
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = snext();
						} while (!isEndOfLine(c));
						return res.toString();
					}
			 
					public boolean isSpaceChar(int c) 
					{
						if (filter != null)
							return filter.isSpaceChar(c);
						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					}
			 
					private boolean isEndOfLine(int c) 
					{
						return c == '\n' || c == '\r' || c == -1;
					}
			 
					public interface SpaceCharFilter
				    {
						public boolean isSpaceChar(int ch);
					}
				}
				
				static class CodeX {
		        public static void sort(long arr[]) {
		            merge_sort(arr, 0, arr.length - 1);
		        }
		
		        private static void merge_sort(long A[], long start, long end) {
		            if (start < end) {
		                long mid = (start + end) / 2;
		                merge_sort(A, start, mid);
		                merge_sort(A, mid + 1, end);
		                merge(A, start, mid, end);
		            }
		
		        }
		
		        private static void merge(long A[], long start,long mid, long end) {
		            long p = start, q = mid + 1;
		            long Arr[] = new long[(int)(end - start + 1)];
		            long k = 0;
		
		            for (int i = (int)start; i <= end; i++) {
		                if (p > mid)
		                    Arr[(int)k++] = A[(int)q++];
		
		                else if (q > end)
		                    Arr[(int)k++] = A[(int)p++];
		
		                else if (A[(int)p] < A[(int)q])
		                    Arr[(int)k++] = A[(int)p++];
		
		                else
		                    Arr[(int)k++] = A[(int)q++];
		            }
		            for (int i = 0; i < k; i++) {
		                A[(int)start++] = Arr[i];
		            }
		
		        }
		
		    }
			}	
			
	
				