How to count the number of times an element appered in entire dataframe?

I have a Pandas DataFrame like this:

pd.DataFrame({'names_1' : ['cat', 'dog', 'elephant'],
              'names_2' : ['rat', 'cat', 'tiger'],
              'names_3' : ['cow', 'monkey', 'cat']})


# Output -

    names_1     names_2    names_3
0   cat         rat        cow
1   dog         cat        monkey
2   elephant    tiger      cat

I want to count the number of time 'cat' appeared in the entire dataset. I know about value_counts() method, but it only counts the element in a specific column. How do I count cat appearance in the entire dataset?

Edit – In my use case, I want to return a dictionary of counts of each element, like this:

{cat:3, dog:1, elephant:1, etc..}

>Solution :

df = pd.DataFrame({'names_1' : ['cat', 'dog', 'elephant'],
                  'names_2' : ['rat', 'cat', 'tiger'],
                  'names_3' : ['cow', 'monkey', 'cat']})
    
occurence = df.stack().value_counts().to_dict()

results in

{'cat': 3, 'rat': 1, 'cow': 1, 'dog': 1, 'monkey': 1, 'elephant': 1, 'tiger': 1}