Logic- Prove ⊢¬p⇒(p⇒(p⇒q)) using Fitch System with no premise.

Question

This question has been bugging me all day. I did it by assuming

(1): ¬(¬p⇒(p⇒(p⇒q))) and (2): using bunches of implication introduction

The first one didn't work out at all. I thought in order to create a contradiction, I will assume ¬(¬p⇒(p⇒(p⇒q))), but all the symbols were implications, thus I figured there's no way I could solve it this way.

As for the second method, by repeatedly using implication introduction, it ended up needing me to prove p⇒q, so I try to use the principle of explosion to create q, but I'm stuck on how to create p and not p solely by p. Plus how does ¬p⇒p work out anyway?

It would truly be lovely if anyone can help me out.

P.S. Sorry for grammatical errors, English is not my mother language.

Answer 1

Solved the problem thanks to people making comments. If I'm not mistaken this is probably right.

1         ¬P         Assumption    ]
2          P         Assumption   ]| 
3          P         Assumption  ]||
4        P^¬P        ^-I(1,3)    |||
5          ⊥         ¬-E(4)      |||
6          Q         ⊥-E(5)      ]||
7        P⇒Q        ⇒-I(3-6)     ]|
8      P⇒(P⇒Q)     ⇒-I(2-7)      ]
9   ¬p⇒(p⇒(p⇒q))   ⇒-I(1-8)