You are given an array of integers distance.

You start at the point (0, 0) on an X-Y plane, and you move distance[0] meters to the north, then distance[1] meters to the west, distance[2] meters to the south, distance[3] meters to the east, and so on. In other words, after each move, your direction changes counter-clockwise.

Return true if your path crosses itself or false if it does not.

 

Example 1:

Input: distance = [2,1,1,2]
Output: true
Explanation: The path crosses itself at the point (0, 1).

Example 2:

Input: distance = [1,2,3,4]
Output: false
Explanation: The path does not cross itself at any point.

Example 3:

Input: distance = [1,1,1,2,1]
Output: true
Explanation: The path crosses itself at the point (0, 0).

 

Constraints:

• 1 <= distance.length <= 105
• 1 <= distance[i] <= 105