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:
def f_pond_skater():
    from heapq import heappush, heappop
    H, W, K = [int(i) for i in input().split()]
    start_row, start_col, target_row, target_col = [int(i) - 1 for i in input().split()]
    Grid = [input() for _ in range(H)]

    heap = []
    dist = [[float('inf')] * W for _ in range(H)]
    dist[start_row][start_col] = 0

    diff = ((0, 1), (1, 0), (0, -1), (-1, 0))
    heappush(heap, (0, start_row, start_col))
    while heap:
        cost, row, col = heappop(heap)
        cost_next = cost + 1

        if row == target_row and col == target_col:
            return cost

        for dr, dc in diff:
            nr, nc = row, col
            for _ in range(K):
                nr += dr
                nc += dc
                if not (0 <= nr < H and 0 <= nc < W) or Grid[nr][nc] == '@':
                    break
                if dist[nr][nc] > cost_next:
                    dist[nr][nc] = cost_next
                    heappush(heap, (cost_next, nr, nc))
                elif dist[nr][nc] == cost_next:
                    continue
                else:
                    break
    return -1

print(f_pond_skater())