Michael Sipser Edition 3 Exercise 1 Question 47 (Page No. 90)

Question

Let $\sum=\{1,\#\}$ and let $Y=\{w|w=x_{1}\#x_{2}\#...\#x_{k}$  $\text{for}$  $k\geq 0,$ $\text{each}$ $ x_{i}\in 1^{*},$ $\text{and}$  $x_{i}\neq x_{j}$ $\text{for}$ $i\neq j\}.$ Prove that $Y$ is not regular.