P16803 [Lanqiao Cup 2026 National Python A] Robot Movement

Xiao Lan placed $2026$ inspection robots on a straight track of length $20260606$. The track can be viewed as a number line segment: the left endpoint is at position $0$, and the right endpoint is at position $20260606$. The $i$-th robot is initially at position $10000i$, and has a label with number $i$ attached. To test the inspection scheduling system of these robots, Xiao Lan started all robots. All robots begin moving at the same time, each with speed $1$ unit length per second. Robots with odd numbers move to the left, and robots with even numbers move to the right. During movement, if two robots meet head-on, they immediately each turn around and continue moving at the original speed. When a robot reaches position $0$ or position $20260606$, it immediately leaves the track and no longer participates in subsequent movement. Xiao Lan records the label numbers on the robots in the order they leave the track. Now compute what the $777$-th recorded label number is.

N/A

This is an output-only fill-in-the-blank problem. You only need to compute the result and submit it. The result is an integer. When submitting, you only need to write a program that outputs this integer; any extra content will not receive points.

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