NASA is studying an unnatural tidal wave phenomenon on a distant planet. They've recorded a sequence of incoming waves represented by an array w. Each wave has a direction and strength:

• The absolute value of each number represents the wave's height in meters.
• The sign indicates the direction: positive means flowing eastward, negative means flowing westward.
• The index in the array represents the wave's position in the observation sequence.

When waves flowing in opposite directions meet, they create a collision. In a collision:

• If one wave is taller than the other, the smaller wave dissipates completely while the taller wave continues its course.
• If both waves are of equal height, they neutralize each other and both dissipate.
• Waves flowing in the same direction never interact with each other.

Given the initial wave measurements, determine which waves will remain after all possible collisions have occurred.

The first line contains an integer $n$ $(1 \leq n \leq 10^5)$, representing the size of array $w$. The second line contains $n$ integers $w_1, w_2, \dots, w_n$, representing the array $w$. $(-10^6 \leq w_i \leq 10^6)$

Give the output as a sequence of integers representing the direction and strength of remaining waves.