| Let there be a set that contains distinct positive integers. To expand the set to contain as many integers as possible, Eri can choose two integers $x\neq y$ from the set such that their average $\frac{x+y}2$ is still a positive integer and isn't contained in the set, and add it to the set. The integers $x$ and $y$ remain in the set. | |
| Let's call the set of integers consecutive if, after the elements are sorted, the difference between any pair of adjacent elements is $1$. For example, sets $\\{2\\}$, $\\{2, 5, 4, 3\\}$, $\\{5, 6, 8, 7\\}$ are consecutive, while $\\{2, 4, 5, 6\\}$, $\\{9, 7\\}$ are not. | |
| Eri likes consecutive sets. Suppose there is an array $b$, then Eri puts all elements in $b$ into the set. If after a finite number of operations described above, the set can become consecutive, the array $b$ will be called brilliant. | |
| Note that if the same integer appears in the array multiple times, we only put it into the set once, as a set always contains distinct positive integers. | |
| Eri has an array $a$ of $n$ positive integers. Please help him to count the number of pairs of integers $(l,r)$ such that $1 \leq l \leq r \leq n$ and the subarray $a_l, a_{l+1}, \ldots, a_r$ is brilliant. | |
| Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. The description of the test cases follows. | |
| The first line of each test case contains a single integer $n$ ($1 \leq n \leq 4 \cdot 10^5$) — length of the array $a$. | |
| The second line of each test case contains $n$ integers $a_1, a_2, \ldots a_n$ ($1 \leq a_i \leq 10^9$) — the elements of the array $a$. | |
| It is guaranteed that the sum of $n$ over all test cases doesn't exceed $4 \cdot 10^5$. | |
| For each test case, output a single integer — the number of brilliant subarrays. | |
| In the first test case, the array $a = [2, 2]$ has $3$ subarrays: $[2]$, $[2]$, and $[2, 2]$. For all of them, the set only contains a single integer $2$, therefore it's always consecutive. All these subarrays are bril |