The gravitational force is a force that attracts any two objects with mass. In this challenge our objects will be Numbers and their mass will be their value. To do so, we don't care about the strength of the force but the direction of it.

Imagine this set of numbers

[1 6 9 4 6 9 7 6 4 4 9 8 7]

Each of them creates an attraction force to it's adjacent numbers. As you may imagine, if the number is bigger than the adjacent it attracts it. Lets take a look at our previous example:

[1 → 6 → 9 ← 4 6 → 9 ← 7 ← 6 ← 4 4 → 9 ← 8 ← 7]

The number 1 is not big enough to attract the number 6, but the number 6 can attract number 1, etc... Basically, numbers are attracted to the biggest adjacent number (also bigger than the number itself). If both of the adjacent numbers are equal it is not attracted then. It also happens when the number and it adjacent are equal.

This is only to show the attraction, but what happens after? Numbers that collide due to attraction are summed up:

[20 32 28]

So basically the challenge is, Given a set of numbers, output the result of the attracted set of numbers.

Example 1

Input  => [10 15 20 10 20 10 10]
          [10 → 15 → 20 10 20 ← 10 10]
Output => [45 10 30 10]

Example 2

Input  => [9 9 9 9 8 1 8]
          [9 9 9 9 ← 8 1 8]
Output => [9 9 9 17 1 8]

Example 3

Input  => [1 6 9 4 6 9 7 6 4 4 9 8 7]
          [1 → 6 → 9 ← 4 6 → 9 ← 7 ← 6 ← 4 4 → 9 ← 8 ← 7]
Output => [20 32 28]

Notes

• Attraction only happens once
• Numbers are not attracted to non-adjacent Numbers