Ambitious Arrangements

How many ways can the integers \(1,1,2,3,4,5,6\) be arranged in a row, so that no integer is immediately adjacent to two strictly larger integers?

Details and assumptions

The sequence \(3, 1, 2, 4, 5, 6, 1\) is not valid as 1 is adjacent to 2 and 3, both of which are strictly larger than 1.
The sequence \( 6, 1, 1, 2, 4, 5 , 3 \) satisfies the conditions of the question. Note that the number 3 is only adjacent to one strictly larger integer.

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