If $x\_1,x\_2,x\_3,x\_4$ are four positive real numbers such that $$x\_1+\frac{1}{x\_2}=4\\x\_2+\frac{1}{x\_3}=1\\x\_3+\frac1{x\_4}=4\\x\_4+\frac1{x\_1}=1$$ then which of the following is true 

1. $x\_1=x\_3$
2. $x\_4=x\_2$
3. $x\_1x\_2=1$
4. $x\_3x\_4=1$