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:
#!/usr/bin/env python3
INF = float("inf")


def main():
    H, W, K = map(int, input().split())
    x1, y1, x2, y2 = map(lambda x: int(x)-1, input().split())
    c = []
    for i in range(H):
        c.append(input())

    DX = [1, 0, -1,  0]
    DY = [0, 1, 0, -1]

    # 方向付きで、ダイクストラ法を使います。
    dist = [[-1]*W for _ in range(H)]
    dist[x1][y1] = 0
    # ヒープでなくて良い。
    # 高々1しか加わっていかないため、キューに加えられた順で十分昇順になる。
    Q = []
    Q.append((0, x1, y1, 0))
    Q.append((0, x1, y1, 1))
    Q.append((0, x1, y1, 2))
    Q.append((0, x1, y1, 3))
    i = 0
    while i < len(Q):
        curr, x, y, DXY = Q[i]
        dx, dy = DX[DXY], DY[DXY]
        for k in range(1, K+1):
            X, Y = x+k*dx, y+k*dy
            if not (0 <= X < H) or not (0 <= Y < W):
                break
            if 0 < dist[X][Y] < curr+1:
                break
            if dist[X][Y] == curr+1:
                continue
            if c[X][Y] == "@":
                break
            dist[X][Y] = curr+1
            Q.append((curr+1, X, Y, (DXY+1) % 4))
            Q.append((curr+1, X, Y, (DXY-1) % 4))
        else:
            Q.append((curr+1, X, Y, DXY))
        if 0 < dist[x2][y2]:
            print(dist[x2][y2])
            return
        i += 1
    print(-1)
    return


if __name__ == '__main__':
    main()