No Time to Dry

Bessie has recently received a painting set, and she wants to paint the long fence at one end of her pasture. The fence consists of $n$ consecutive $1$-meter segments. Bessie has $n$ different colors available, which she labels with the numbers $1$ through $n$ in increasing order of darkness ($1$ is a very light color, and $n$ is very dark). She can therefore describe the desired color she wants to paint each fence segment as an array of $n$ integers.

Initially, all fence segments are uncolored. Bessie can color any contiguous range of segments with a single color in a single brush stroke as long as she never paints a lighter color over a darker color (she can only paint darker colors over lighter colors).

For example, an initially uncolored segment of length four can be colored as follows:

0000 -> 1110 -> 1122 -> 1332

Unfortunately, Bessie doesn't have time to waste watching paint dry. Thus, Bessie thinks she may need to leave some fence segments unpainted! Currently, she is considering $q$ candidate ranges, each described by two integers ($a$, $b$) with 1 \le a \le b \le n giving the indices of endpoints of the range $a$...$b$ of segments to be painted.

For each candidate range, what is the minimum number of strokes needed to paint every fence segment inside the range with its desired color while leaving all fence segments outside the range uncolored? Note that Bessie does not actually do any painting during this process, so the answers for each candidate range are independent.

1 1 2 

2 1 1 2

1 2 2 1 1 2

1 2 3 2