Sequential Clamp

You are given $N$ pairs of integers. The $i$-th pair is denoted $(A_i, B_i)$. It's guaranteed that $A_i \le B_i$ for every $1 \le i \le N$. For an integer $X$, we define $f(X)$ to be the result of the following process: - Let $Y$ be a variable. Initially, $Y = X$. - For each $i = 1, 2, \ldots, N$ **in order**, - If $Y \lt A_i$, set $Y = A_i$. - If $Y \gt B_i$, set $Y = B_i$. - If