Selecting and Sorting column values into columns in new DataFrame

I have a DataFrame that contains words and their bounding boxes on an image, the image is that of a table

df_text = pd.DataFrame({
    'words': ['Hello', 'world', 'nice day', 'have a', 'Greeting_1', 'Greeting_2'],
    'left': [1097, 1099, 258, 259, 1096, 260],
    'top': [1248, 1249, 1156, 1153,1200,250],
    'right': [1154, 1156, 615, 614, 1150, 610],
    'bottom': [1269, 1271, 1175, 1172, 1255, 1170] 
})

Which looks like this:

Words           left     top      right     bottom
hello           1097     1248     1154      1269
world           1099     1249     1156      1271
nice day        258      1156     615       1175
have a          259      1153     614       1172
Greeting_1      1096     1200     1150      1255
Greeting_2      260      250      610       1170

I now want to create a DataFrame that mimics the original image which looks like this:

Greeting_1            Greeting_2
hello                 Have a  
world                 nice day

So basically I want to select the column values of words that come under Greeting_1 and make a new column out of it and want the same for Greeting_2. Generally the left, top, right, bottom values of Greeting_1 and Greeting_2 are lower than the words that come under it. Greeting_1 and Greeting_2 can appear in any order in the original dataframe.

Would appreciate some help in solving this problem.