7,8,9 |

In a deck of 16 cards, numbered from top to bottom. It is allowed to take a portion of the deck from the top, after which the removed and remaining parts of the deck, without flipping, are "interleaved" with each other. Can it happen that after several such operations, the cards end up numbered from bottom to top? If yes, in what minimum number of operations can this occur?
Let's consider a method that allows achieving the required order in four operations. Each time, we will take exactly half of the deck - 8 cards from the top and "interleave" the removed part into the remaining part "one by one". The transformation of the deck during such operations is shown in the diagram:

| Top |  | 1 | 1 |  |  |  |  |  |  |  |  | Bottom |  |  |  |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 9 | 1 | 10 | 2 | 11 | 3 | 12 | 4 | 13 | 5 | 14 | 6 | 15 | 7 | 16 | 8 |
| 13 | 9 | 5 | 1 | 14 | 10 | 6 | 2 | 15 | 11 | 7 | 3 | 16 | 12 | 8 | 4 |
| 15 | 13 | 11 | 9 | 7 | 5 | 3 | 1 | 16 | 14 | 12 | 10 | 8 | 6 | 4 | 2 |
| 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |

Consider any three operations on the deck that satisfy the condition. During each operation, the deck is divided into two parts: the part that is removed and the part that remains. Since there are 16 cards in total, one of these parts contains at least eight cards. A similar reasoning shows that among these cards, there will be at least four cards that, during the second operation, were either all in the removed part of the deck or all in the remaining part. And among them, in turn, there will be two cards that ended up in the same part during the third operation. Thus, we have found two cards that, in all operations, were either removed or remained in

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