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:
# coding: utf-8
import sys
from heapq import heapify, heappop, heappush

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

H, W, K = lr()
SX, SY, GX, GY = lr()
SX -= 1; SY -= 1; GX -= 1; GY -= 1
pond = [sr() for _ in range(H)]
INF = 10 ** 10

def to_ID(x, y, con):
    return (x*W + y) * 4 + con

def mod_ceil_K(x):
    return (x+K-1) // K * K

def push(d, id):
    if dist[id] < d:
        return
    dist[id] = d
    heappush(que, (d, id))    

dist = [INF] * (H*W*4)
start = to_ID(SX, SY, 0)
dist[start] = 0
que = [(0, start)]
UDLR = [(0, -1), (1, 0), (0, 1), (-1, 0)]
goal = to_ID(GX, GY, 0)
while que:
    d, id = heappop(que)
    if id == goal:
        answer = mod_ceil_K(d) // K
        print(answer); exit()
    if dist[id] < d:
        continue
    x = id // 4 // W
    y = id // 4 % W
    con = id % 4
    for i in range(4):
        next_id = to_ID(x, y, i)
        if dist[next_id] > mod_ceil_K(d):
            push(mod_ceil_K(d), next_id)
    dx = UDLR[con][0]; dy = UDLR[con][1]
    nx = x + dx; ny = y + dy
    if not (0 <= nx < H and 0 <= ny < W) or pond[nx][ny] == '@':
        continue
    next_id = to_ID(nx, ny, con)
    if dist[next_id] > d + 1:
        dist[next_id] = d + 1
        push(d+1, next_id)
    
print(-1)