Problem: Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with H east-west rows and W north-south columns. Let (i,j) be the square at the i-th row from the north and j-th column from the west.

Some of the squares have a lotus leaf on it and cannot be entered. The square (i,j) has a lotus leaf on it if c_{ij} is `@`, and it does not if c_{ij} is `.`.

In one stroke, Snuke can move between 1 and K squares (inclusive) toward one of the four directions: north, east, south, and west. The move may not pass through a square with a lotus leaf. Moving to such a square or out of the pond is also forbidden.

Find the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2). If the travel from (x_1,y_1) to (x_2,y_2) is impossible, point out that fact.

Constraints

* 1 \leq H,W,K \leq 10^6
* H \times W \leq 10^6
* 1 \leq x_1,x_2 \leq H
* 1 \leq y_1,y_2 \leq W
* x_1 \neq x_2 or y_1 \neq y_2.
* c_{i,j} is `.` or `@`.
* c_{x_1,y_1} = `.`
* c_{x_2,y_2} = `.`
* All numbers in input are integers.

Input

Input is given from Standard Input in the following format:


H W K
x_1 y_1 x_2 y_2
c_{1,1}c_{1,2} .. c_{1,W}
c_{2,1}c_{2,2} .. c_{2,W}
:
c_{H,1}c_{H,2} .. c_{H,W}


Output

Print the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2), or print `-1` if the travel is impossible.

Examples

Input

3 5 2
3 2 3 4
.....
.@..@
..@..


Output

5


Input

1 6 4
1 1 1 6
......


Output

2


Input

3 3 1
2 1 2 3
.@.
.@.
.@.


Output

-1

Solution (in PYTHON3):

Solution:
H,W,K=map(int,input().split())
x1,y1,x2,y2=map(int,input().split())
C=[]
nx=set([])

for _ in range(H):
    C.append(list(input()))

def keiro(x,y,k):
    i=1
    while True:
        if y+i>W-1 or C[x][y+i]!='.' or i>k:
            break
        else:
            if (x,y+i) not in nx:
                nx.add((x,y+i))
            i+=1
    
    i=1
    while True:
        if y-i<0 or C[x][y-i]!='.' or i>k:
            break
        else:
            if (x,y-i) not in nx:
                nx.add((x,y-i))
            i+=1
    
    i=1
    while True:
        if x+i>H-1 or C[x+i][y]!='.' or i>k:
            break
        else:
            if (x+i,y) not in nx:
                nx.add((x+i,y))
            i+=1
    
    i=1
    while True:
        if x-i<0 or C[x-i][y]!='.' or i>k:
            break
        else:
            if (x-i,y) not in nx:
                nx.add((x-i,y))
            i+=1

    return 0

C[x1-1][y1-1]=0
keiro(x1-1,y1-1,K)
taisho=nx.copy()
result=1
for j in nx:
    C[j[0]][j[1]]=result

while C[x2-1][y2-1]=='.':
    nx=set([])
    if len(taisho)==0 or result>10**6:
        result=-1
        break
    for l in taisho:
        keiro(l[0],l[1],K)
    result+=1
    for j in nx:
        C[j[0]][j[1]]=result
    taisho=nx.copy()

print(result)