How do I find all the fixed points of a...

How do I find the number of fixed points in a randomly increasing sequence of integers in O(log n) time?
(1 1 1 1 5 7) as input will return 1. Because 5 is the fifth element.

Consider this example instead of the erroneous example given above.
Input: {-1, 0, 2, 4, 5, 6, 7}
Output: 4
I need an algorithm to find the number of fixed points of an increasing sequence in O(log n) time.
Yes. The sequence is known beforehand.
I was considering something like a binary search, but it would take more than O(log n) to find the number of fixed points.
So currently I am thinking of using something like an averaging scheme, but I haven't found any solution yet.

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