You are given an n x n integer matrix grid where each value grid[i][j] represents the elevation at that point (i, j).

The rain starts to fall. At time t, the depth of the water everywhere is t. You can swim from a square to another 4-directionally adjacent square if and only if the elevation of both squares individually is at most t. You can swim infinite distances in zero time. Of course, you must stay within the boundaries of the grid during your swim.

Return the least time until you can reach the bottom right square (n - 1, n - 1) starting from the top left square (0, 0).

Examples

Example 1

Input:  grid = [[0,2],[1,3]]
Output: 3

At time 3, we can swim anywhere since all elevations ≤ 3. The path is (0,0) → (1,0) → (1,1).

Example 2

Input:  grid = [[0,1,2,3,4],[24,23,22,21,5],[12,13,14,15,16],[11,17,18,19,20],[10,9,8,7,6]]
Output: 16

We need to wait until time 16 so we can follow the path around the border.

Constraints

• n == grid.length == grid[i].length
• 1 <= n <= 50
• 0 <= grid[i][j] < n * n
• Each value in grid is unique