Pushpa CodeChef Solution | CodeChef Problem Solution 2022

Pushpa CodeChef Solution | CodeChef Problem Solution 2022

Pushpa has entered Chefland and wants to establish Pushpa-Raj here too.

Chefland consists of N$N$ floating wooden logs. Each log has a positive integer written on it which denotes the height of the log from ground. The ith$i^{th}$ wooden log is initially floating at a height Hi$H_i$ from the ground.

Pushpa will initially start by jumping on any wooden log of his choice. He has the power to jump any horizontal distance, but he can jump from a wooden log at height X$X$ to a wooden log at height (X+1)$(X+1)$ only.

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Moreover, in Chefland, gravitational pull is affected by the jumps made and as a result when Pushpa jumps on a wooden log A$A$, then the wooden log A$A$ first sinks by 1$1$ unit and then all the wooden logs rise by 1$1$ unit. More formally, wooden log A$A$ maintain its height whereas rest logs rise by 1$1$ unit.

To establish his rule, Pushpa wants to achieve the maximum height possible. Determine the maximum height he will achieve from the ground.

Input Format

• The first line contains a single integer T$T$ - the number of test cases. Then the test cases follow.

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• The first line of each test case contains an integer N$N$ - the number of wooden logs.
• The second line of each test case contains N$N$ space-separated integers H1,H2,…,HN$H_1,H_2,\dots ,H_N$ denoting the initial heights of the logs from the ground.

Output Format

For each testcase, output in a single line the maximum height achieved by Pushpa.

Constraints

• 1≤T≤10$1\le T\le 10$
• 1≤N≤105$1\le N\le {10}^5$
• 1≤Hi≤109$1\le H_i\le {10}^9$

Sample Input 1 

2
4
1 2 1 3
1
2

Sample Output 1 

3
2

Explanation

• Test case 1$1$: If Pushpa chooses to start from wooden log at index 1$1$ with height of 1$1$ units, then the new heights will be [1,3,2,4]$[1,3,2,4]$. He can then jump to log at height 2$2$ units after which he is unable to make any jumps. To achieve the maximum height, he chooses wooden log at height 3$3$ and achieves a height of 3$3$ units.
• Test case 2$2$: There is only 1$1$ wooden log so Pushpa reaches the height of 2$2$ units.

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