Help me save my mangoes from neighbors!!!?

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Help me save my mangoes from neighbors!!!?

My story is a bit long…but please bear with me

Info about victim: In our backyard we have a 20feet+ mango tree which my grandfather planted when he was a teenager…(about 50 years ago from now)…It gives fruit in alternative years…only we take care of the tree…the neighbors don’t give an eye to it rest of the year…The base of our tree is completely on our property however some of its branches are just above the roof of our neighbors’ house…

From many years i have been noticing that my neighbors are taking advantage of my tree. All three of our neighbors have a mango tree too but the fruit their tree bears is not so sweet and quantity is also less…They pluck mangoes from our tree whenever it gives fruit(at all alternative years)….all this they do is without our permission(by undue influence of relationship and morals)…

BUT when I do the same with their tree they start screaming at me, disallowing me to pluck any single of it…not only this, they also start spreading bad words about me like: the boy has no atticates, he was stealing from our tree, the boy is not tought right and all that non sense which is completely false (as per my teachers, parents and even by strangers who whom i never met).. The tree is at a place where i can’t use barbed wires or fences… I have a Dog in my house ..I tried using it, but they often steal at night or when i take my dog for a walk….Its for sure they’re stealing it…I have their pics too(evidence)…I am not suing them because it sounds a bit too much and due to mutual friends…

THE BITTER PART OF STORY: The neighbors living behind our house once tried to cut off our tree saying: ,”the roots of your tree are damaging the construction (base) of our house and our house is getting water from beneath the floor, we’ll have to cut this tree”..THIS WAS COMPLETELY A LIE!
I went to their house and saw it was nothing as they said…they were simply jealous….In the same year when our tree gave fruit they were the first to pluck them (in a very large quantity)…. I don’t say i don’t wanna share my fruits but this is too much!…about 75% of our mangoes are consumed by them, 10% are distributed by them to their loved ones(to earn goodwill) and 15% or less are received by us…

Should i go to police? will it not be too much? does anyone has a better idea? please help me…It has been a problem from the time i took birth…really…Isn’t there a human repelling spray? Should i beat them on street? answers will be really appreciated…
@Cho Duffield: I agree some of the branches are not in our property… Literally the are ABOVE the roof of our neighbors house…Not even a single branch touches their house(fence/ roof)…They use bamboos(or whatever) to pluck mangoes…
I disagree with u….The roots of mango tree goes simply downward(unlike other trees)…The tree wasn’t damaging their property…Infact the tree was there even before their house was built…AND cutting, they wanted to completely chop the tree from top to bottom…
@T rexs: No doubt the roots aren’t in their property…The tree is at a sufficient distance that roots cannot go there…Only some branches are hanging over their property…And one more thing…its not about going to one’s yard, its about going to one’s roofs… all 4 roofs are someway connected to each other…anyone can easily jump from one to another…the tree is in the center…I doubted police won’t do anything that is why i didn’t went…