BaoBao is playing the famous gameElden Ringthese days. It's an open-world game in which you can control your character to travel from places to places. However, your character could also enter a trap and you need to figure out how to escape. Right now, BaoBao's character is stuck in a 2-dimensional plane with deadly lasers. There are nnn laser generators shooting laser beams between every pair of them . The beams start and end at generator points and do not stretch to infinity. Starting at point (0,0)(0,0)(0,0), BaoBao wants to escape to point without touching any laser beam or generator. In order to do so, BaoBao can ask her friend DreamGrid to remove any number of laser generators, together with any laser beam that starts or ends at these generators. Output the minimum number of laser generators that need to be erased for the escape. Note that BaoBao does not need to move in a specific direction to escape. Her escaping route can even be a curve if necessary.
BaoBao is playing the famous gameElden Ringthese days. It's an open-world game in which you can control your character to travel from places to places. However, your character could also enter a trap and you need to figure out how to escape. Right now, BaoBao's character is stuck in a 2-dimensional plane with deadly lasers. There are nnn laser generators (each can be regarded as a point) shooting laser beams between every pair of them (so there are n(n−1)2frac{n(n-1)}{2}2n(n−1) laser beams in total). The beams start and end at generator points and do not stretch to infinity. Starting at point (0,0)(0,0)(0,0), BaoBao wants to escape to point (1010101010,1010101010)(10^{10^{10^{10^{10}}}}, 10^{10^{10^{10^{10}}}})(1010101010,1010101010) without touching any laser beam or generator. In order to do so, BaoBao can ask her friend DreamGrid to remove any number of laser generators, together with any laser beam that starts or ends at these generators. Output the minimum number of laser generators that need to be erased for the escape. Note that BaoBao does not need to move in a specific direction to escape. Her escaping route can even be a curve if necessary.