[Solution] Good Subarrays (Easy Version) Codeforces Solution

C1. Good Subarrays (Easy Version)

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

This is the easy version of this problem. In this version, we do not have queries. Note that we have multiple test cases in this version. You can make hacks only if both versions of the problem are solved.

An array 𝑏$b$ of length 𝑚$m$ is good if for all 𝑖$i$ the 𝑖$i$-th element is greater than or equal to 𝑖$i$. In other words, 𝑏$b$ is good if and only if 𝑏𝑖≥𝑖$b_i\ge i$ for all 𝑖$i$ (1≤𝑖≤𝑚$1\le i\le m$).

You are given an array 𝑎$a$ consisting of 𝑛$n$ positive integers. Find the number of pairs of indices (𝑙,𝑟)$(l,r)$, where 1≤𝑙≤𝑟≤𝑛$1\le l\le r\le n$, such that the array [𝑎𝑙,𝑎𝑙+1,…,𝑎𝑟]$[a_l,a_{l+1},\dots ,a_r]$ is good.

Input

Each test contains multiple test cases. The first line contains the number of test cases 𝑡$t$ (1≤𝑡≤2⋅105$1\le t\le 2\cdot {10}^5$). Description of the test cases follows.

The first line of each test case contains an integer 𝑛$n$ (1≤𝑛≤2⋅105$1\le n\le 2\cdot {10}^5$), the length of the array 𝑎$a$.

The second line of each test case contains 𝑛$n$ space-separated integers 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ (1≤𝑎𝑖≤𝑛$1\le a_i\le n$), representing the array 𝑎$a$.

It is guaranteed that the sum of 𝑛$n$ over all test cases does not exceed 2⋅105$2\cdot {10}^5$.

Output

For each test case, print the number of suitable pairs of indices.

Note

In the first test case, all subarrays of 𝑎$a$ are good, so all pairs are suitable.

In the second test case, the pairs (1,1)$(1,1)$, (2,2)$(2,2)$, and (3,3)$(3,3)$ are suitable. For example, when (𝑙,𝑟)=(1,2)$(l,r)=(1,2)$, the array 𝑏=[1,1]$b=[1,1]$ is not good because 𝑏2<2$b_2<2$.