Sum3

Problem code: ENCODE13

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You're given an array 'a' of N distinct integers. Let's consider a triple ( i, j, k ), 0 <= i < j < k <= N-1. The sum of corresponding elements is equal to a[i]+a[j]+a[k]. For all the possible sums you can get by choosing such a triple output its value and the number of triples that result in such a sum.

Input

The first line of input contains an integer N (3 <= N <= 20000). Each of the next N lines contain an integer a[i] (|a[i]| <= 10000).

Output

Output each of the possible sums in increasing order with the number of triples that generate them. The format should be: s[i] : ways[i] (s[i] = value of the i-th sum, ways[i] = number of triples that generate it)

Example

Input:
4
-1
2
3
4


Output:
4 : 1
5 : 1
6 : 1
9 : 1


Constraints:

3 <= N <= 20000
|a[i]| <= 10000 for all i.

Author: encoded_admin
Date Added: 23-02-2011
Time Limit: 3 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, C, C99 strict, CLOJ, CPP 4.0.0-8, CPP 4.3.2, CS2, D, F#, FORT, GO, ICON, JAR, JAVA, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PHP, PIKE, PYTH, PYTH 3.1.2, RUBY, SCM guile, SCM qobi, ST, TCL


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