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This version of the problem differs from the previous one only in the constraint on $t$. You can make hacks only if both versions of the problem are solved.

You are given two positive integers $l$ and $r$.

Count the number of distinct triplets of integers $(i, j, k)$ such that $l \le i \lt j \lt k \le r$ and $\operatorname{lcm}(i,j,k) \ge i + j + k$.

Here $\operatorname{lcm}(i, j, k)$ denotes the least common multiple (LCM) of integers $i$, $j$, and $k$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($\bf{1 \le t \le 10^5}$). Description of the test cases follows.

The only line for each test case contains two integers $l$ and $r$ ($1 \le l \le r \le 2 \cdot 10^5$, $l + 2 \le r$).

Output

For each test case print one integer — the number of suitable triplets.

Note

In the first test case, there are $3$ suitable triplets:

• $(1,2,3)$,
• $(1,3,4)$,
• $(2,3,4)$.

In the second test case, there is $1$ suitable triplet:

• $(3,4,5)$.