Problem: Takahashi is locked within a building.

This building consists of H×W rooms, arranged in H rows and W columns. We will denote the room at the i-th row and j-th column as (i,j). The state of this room is represented by a character A_{i,j}. If A_{i,j}= `#`, the room is locked and cannot be entered; if A_{i,j}= `.`, the room is not locked and can be freely entered. Takahashi is currently at the room where A_{i,j}= `S`, which can also be freely entered.

Each room in the 1-st row, 1-st column, H-th row or W-th column, has an exit. Each of the other rooms (i,j) is connected to four rooms: (i-1,j), (i+1,j), (i,j-1) and (i,j+1).

Takahashi will use his magic to get out of the building. In one cast, he can do the following:

* Move to an adjacent room at most K times, possibly zero. Here, locked rooms cannot be entered.
* Then, select and unlock at most K locked rooms, possibly zero. Those rooms will remain unlocked from then on.



His objective is to reach a room with an exit. Find the minimum necessary number of casts to do so.

It is guaranteed that Takahashi is initially at a room without an exit.

Constraints

* 3 ≤ H ≤ 800
* 3 ≤ W ≤ 800
* 1 ≤ K ≤ H×W
* Each A_{i,j} is `#` , `.` or `S`.
* There uniquely exists (i,j) such that A_{i,j}= `S`, and it satisfies 2 ≤ i ≤ H-1 and 2 ≤ j ≤ W-1.

Input

Input is given from Standard Input in the following format:


H W K
A_{1,1}A_{1,2}...A_{1,W}
:
A_{H,1}A_{H,2}...A_{H,W}


Output

Print the minimum necessary number of casts.

Examples

Input

3 3 3
#.#
#S.
###


Output

1


Input

3 3 3
.#
S.


Output

1


Input

3 3 3

S#


Output

2


Input

7 7 2


...##
S###
.#.##
.###


Output

2

Solution (in CPP):

Solution:
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>
#define pii pair<int,int>
#define mp make_pair
using namespace std;
int n,m,k,cx,cy,ans=1e9;
char s[805][805];
int d[805][805];
const int dx[]={0,1,-1,0},dy[]={1,0,0,-1};
void bfs()
{
	queue<pii> q;
	q.push(mp(cx,cy));d[cx][cy]=0;
	while(!q.empty())
	{
		int x=q.front().first,y=q.front().second;
		q.pop();
		for(int i=0;i<4;i++)
		{
			int nx=x+dx[i],ny=y+dy[i];
			if(d[nx][ny]<=d[x][y]+1||s[nx][ny]=='#')continue;
			d[nx][ny]=d[x][y]+1;
		    q.push(mp(nx,ny));
	    }
	}
}
int main()
{
	scanf("%d%d%d",&n,&m,&k);
	for(int i=1;i<=n;i++)
	{
		scanf("%s",s[i]+1);
		for(int j=1;j<=m;j++)
		{if(s[i][j]=='S')cx=i,cy=j,s[i][j]='.';d[i][j]=1e9;} 
	}
	bfs();
	for(int i=1;i<=n;i++)
	for(int j=1;j<=m;j++)
	if(d[i][j]<=k)
	ans=min(ans,1+(min(min(i-1,n-i),min(j-1,m-j))+k-1)/k);
	printf("%d\n",ans);
	return 0;
}