Infix to prefix

Question

What is the stack size while implementing this infix to postfix expression using operator stack?

a+b+c+d+e

Comments

According to me it's 1...

But if the expression is like this

 

A^B^C^D^E

Then how many stack units ?

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$a^{(b^{(c^{(d^e)})})}$

I think all the power operators will be on the stack because of right to left associative nature

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kindly explian?