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<algorithm>
using namespace std;
int Q[1010000][2], head, tail, D[810][810];
int n, m, K, sx, sy;
char p[810][810];
void Ins(int x, int y, int d){
    if(D[x][y]<=d || p[x][y]!='.')return;
    D[x][y]=d;
    tail++;
    Q[tail][0]=x,Q[tail][1]=y;
}
int main(){
    int i, j, x, y;
    scanf("%d%d%d",&n,&m,&K);
    for(i=1;i<=n;i++){
        scanf("%s",p[i]+1);
        for(j=1;j<=m;j++){
            if(p[i][j]=='S')sx=i,sy=j,p[i][j]='.';
            D[i][j]=1e9;
        }
    }
    Ins(sx,sy,0);
    while(head < tail){
        head++;
        x = Q[head][0], y = Q[head][1];
        Ins(x+1,y,D[x][y]+1);
        Ins(x,y+1,D[x][y]+1);
        Ins(x-1,y,D[x][y]+1);
        Ins(x,y-1,D[x][y]+1);
    }
    int res = 1e9;
    for(i=1;i<=n;i++){
        for(j=1;j<=m;j++){
            if(D[i][j] <= K){
                res = min(res,1 + (min(min(i-1, n-i), min(j-1, m-j)) + K-1)/K);
            }
        }
    }
    printf("%d\n",res);
}