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Itachi and Sasuke are trying to beat Kabuto, the caster of an awesome magical spell (or you can say jutsu). Kabuto has a power level of **N**. The fight between them is quite weird. There’s a bag with some potions that contain power. There are exactly **N** potions in the bag and the **i’th** potion has a power level of **i** (**i** starts from **1**).

Itachi and Sasuke each pull out a random potion from the bag simultaneously. If the power level of each of their potions is **co-prime** with **N** and the sum of their power levels is greater than **N**, then Itachi and Sasuke say to Kabuto, **“Omae Wa Mou Shindeiru”**. Kabuto then shouts, **“NANI???”** and dies with a poof!!!

As you are a great mathematician and programmer and they are not, can you tell what is the probability that Itachi and Sasuke can say, **“Omae Wa Mou Shindeiru”???**

There will be several test cases. The first line will contain an integer **T (1 <= T <= 1000)** denoting the number of test cases.

The next **T** lines each will contain an integer **N (2 <= N <= 10 ^{15})**, the power level of Kabuto.

The inputs are randomly generated.

For each test case, print the probability of Itachi and Sasuke saying “Omae Wa Mou Shindeiru” in a new line. Your answer should be rounded to exactly **10** digits after the decimal.

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

2 2 3 | 0.0000000000 0.0000000000 |

78% Solution Ratio

NirjhorEarliest,

NirjhorFastest, 0.0s

NirjhorLightest, 131 kB

magic_kiriShortest, 1970B

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