Triangle

The problem is to find the minimum path sum from top to bottom if given a triangle. Each step you may move to adjacent numbers on the row below.

Input & Output

Input

triangle — see example

Output

the minimum path sum

Example

Input

triangle = [
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

Output

Explanation

The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11.

Try it yourself