CRZYSMKR - Crazy Smoker

The "BHAI Group" Of IIIT Allahabad is Famous For Many Things, Leading in Every Field Of College Activity

So One Day The Leader Of Bhai Group decided to smoke C(N) cigarettes each day:

  • F(N) = 34N + (30 × N) + 32
  • C(N) = F(N) mod 11, where x mod y is the remainder obtained by dividing x by y.

But Bhai Group's Leader's Girlfriend wants that he doesn't smoke any cigarettes, so she made a modification:

  • F(N) = 34N + (30 × N) + (32 + M)
  • C(N) = F(N) mod 11

Input

First line of each test case is an integer T, total number of test cases. Next T lines contains a single integer N.

Output

Print the minimum value of M in single line for each test case.

Constraints

1 ≤ T ≤ 106

1 ≤ N ≤ 1018

Example

Input:
2
1
2

Output:
3
6

Explanation

For N = 1, F(N) = 34 + 30 + 32 = 96. So, M = 3, now C(N) = 99 mod11 = 0.

For N = 2, F(N) = 1156 + 60 + 32 = 1248. So, M = 6, now C(N) = 1254 mod11 = 0

Problem Credits : IIIT Allahabad HE Club


Added by:Siddharth Singh
Date:2016-02-10
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY
Resource:HackerEarth Contest Of IIIT Allahabad

hide comments
2018-12-29 10:46:38 Robert Gawron
No need to calculate 34^N, because 34^N % 11 is always 1 and (a+b+c)%N = a%N +b%N +c%N
2018-06-19 12:48:19
nice mathematics
2018-02-22 11:55:35
Don't believe spojtoolkit for this one.
2017-12-05 13:14:04
Super easy, just follow modular arithmetic closely!!

Last edit: 2017-12-05 13:15:05
2017-05-28 20:10:00
AC in a GO!!
Just the Binomial Expansion....and its done!!
2017-02-02 15:36:55
those who know binomial expansion can do it in easily !
2017-01-06 11:59:33
34^(10^18) is beyond C limits, costed me 2 WA.
2016-11-01 13:07:47 Shashank Tiwari
Let me simplify the stupid problem statement :

Find minimum non negative 'M' such that

(34^N + 30*N + 32 +M )%11 = 0

Last edit: 2016-11-01 13:08:38
2016-08-18 13:57:20
Sily Mistake cost me 2 WA .. otherwise should be moved in basics too easy
2016-07-30 08:51:15
observe the pattern..:D
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.