[Solution] Infinity Staircase CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Infinity Staircase CodeChef Solution | CodeChef Problem Solution 2022

You are climbing an infinity staircase, which (as its name suggests) has an infinite number of steps. You are currently standing at the 1$1$st step, and you would like to reach the N$N$-th step. When standing at the i$i$-th step, you can make one of the following three moves:

• Move to step i+1$i+1$
• Move to step i+2$i+2$
• Move to step i+3$i+3$

However, you can't make the same move twice in a row.

For example, suppose you reach the 7$7$th step from the 4$4$th step using the third move. Then, from the 7$7$th step, you can move to either the 8$8$th or the 9$9$th step (using the 1$1$st or 2$2$nd move) — but you can't move to the 10$10$th step (because you would use the third move twice in a row). 

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Now suppose you choose the 1$1$st move and move to the 8$8$th step. On your next move, you cannot move to the 9$9$th step, but you can move to either the 10$10$th or the 11$11$th step.

Under these conditions, find the minimum number of moves you need to reach the N$N$-th step.

Input Format

• The first line of input will contain a single integer T$T$, denoting the number of test cases.

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• Each test case consists of a single line containing one integer, N$N$.

Output Format

• For each test case, print on a new line the minimum number of moves required to reach the N$N$-th step.

Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 1≤N≤109