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Have you played the game Spot it!? Though there are many ways to play this game, the basic rule is the same for all - find the matching element between two cards.

In a classic deck of Spot it! there are 55 cards, each containing 8 different symbols. And there is a very interesting property. Any 2 cards have exactly one symbol in common.

This makes many people wonder: how many symbols are sufficient to make those 55 cards?

Let us be more generic and find out:

How many symbols are sufficient to make a deck of N cards?

So that in a deck of N cards:

- All cards contain the same number of symbols.
- Any 2 of the cards has exactly 1 symbol in common.
- Each card has more than 1 symbol and
- All symbols in a single card are different.

An integer `$T$`

(`$1 \le T \le 100$`

) denoting the number of test cases to follow.

Each of the next T lines will have an integer `$N$`

(`$1 \le N \le 10^4$`

).

For each test case, print the minimum number of symbols required in a new line.

Input | Output |
---|---|

2 6 30 | 7 31 |