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:
import sys
from collections import deque
sys.setrecursionlimit(10000000)
readline = sys.stdin.readline

def solve():
    H, W, K = map(int, readline().split())
    x1, y1, x2, y2 = map(int,readline().split())
    x1, y1, x2, y2 = (v - 1 for v in (x1, y1, x2, y2))
    C = [readline().rstrip() for i in range(H)]

    INF = 10 ** 10
    visited = [[INF] * W for i in range(H)]
    dist = [[0] * W for i in range(H)]

    dirs = [(1, 0), (0, 1), (-1, 0), (0, -1)]

    q = deque()

    q.append((x1, y1, 0))
    visited[x1][y1] = 0
    dist[x1][y1] = 0

    def aa(_i, _j, y, x, d):
        i, j = _i, _j
        for k in range(K):
            i += y
            j += x
            if not (0 <= i < H and 0 <= j < W):
                break
            if C[i][j] == '@':
                break
            if d > visited[i][j]:
                break
            if d == visited[i][j]:
                continue
            visited[i][j] = d
            dist[i][j] = d
            q.append((i, j, d))

    while q:
        i, j, d = q.popleft()
        for y,x in dirs:
            aa(i, j, y, x, d+1)
    
    if visited[x2][y2] == INF:
        print(-1)
    else:
        print(dist[x2][y2])
    
solve()