F. Antennastime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere are n equidistant antennas on a line, numbered from 1 to n. Each antenna has a power rating, the power of the i-th antenna is p_i. The i-th and the j-th antenna can communicate directly if and only if their distance is at most the minimum of their powers, i.e., |i-j| \leq \min(p_i, p_j). Sending a message directly between two such antennas takes 1 second.What is the minimum amount of time necessary to send a message from antenna a to antenna b, possibly using other antennas as relays?InputEach test contains multiple test cases. The first line contains an integer t (1\le t\le 100\,000) — the number of test cases. The descriptions of the t test cases follow.The first line of each test case contains three integers n, a, b (1 \leq a, b \leq n \leq 200\,000) — the number of antennas, and the origin and target antenna. The second line contains n integers p_1, p_2, \dots, p_n (1 \leq p_i \leq n) — the powers of the antennas.The sum of the values of n over all test cases does not exceed 200\,000. OutputFor each test case, print the number of seconds needed to trasmit a message from a to b. It can be shown that under the problem constraints, it is always possible to send such a message.ExampleInput
310 2 94 1 1 1 5 1 1 1 1 51 1 113 1 33 3 1Output
4
0
2
NoteIn the first test case, we must send a message from antenna 2 to antenna 9. A sequence of communications requiring 4 seconds, which is the minimum possible amount of time, is the following:   In 1 second we send the message from antenna 2 to antenna 1. This is possible since |2-1|\le \min(1, 4) = \min(p_2, p_1).  In 1 second we send the message from antenna 1 to antenna 5. This is possible since |1-5|\le \min(4, 5) = \min(p_1, p_5).  In 1 second we send the message from antenna 5 to antenna 10. This is possible since |5-10|\le \min(5, 5) = \min(p_5, p_{10}).  In 1 second we send the message from antenna 10 to antenna 9. This is possible since |10-9|\le \min(5, 1) = \min(p_{10}, p_9). 
310 2 94 1 1 1 5 1 1 1 1 51 1 113 1 33 3 1
4 0 2 
['data structures', 'dfs and similar', 'graphs', 'graphs', 'implementation', 'implementation', 'shortest paths', 'shortest paths']