KSEQ - 123 Sequence
A 123 sequence is defined as a non-decreasing sequence of length>=2, where each number is 1 or 2 or 3. The difference between all unique pairs of numbers is given i.e. for a 123 sequence a1, a2, a3, ... and the differences are aj-ai for 1 <= i < j <= n.
Since the 123 sequence contains only 1, 2, 3 the difference between any pair can be 0, 1, 2. Given the number of 0s, 1s, 2s in the difference sequence X, Y, Z respectively, your task is to find the number of distinct 123 sequences that could result in X, Y, Z.
Two 123 sequences A and B are considered different if there exists at least one i such that Ai is not equal to Bi.
Input
First line of the input contains the number of test cases T. (T <= 10000). Then follow T lines each containing 3 space separated integer X, Y, Z. (0 <= X, Y, Z <=108. X+Y+Z > 0).
Output
For each test case output the number of distinct 123 sequences in a separate line.
Example
Input:
3
0 2 1
1 2 3
1 3 2
Output:
1
0
2
Explanation
For the third test case the 123 sequences are 1, 2, 3, 3 and 1, 1, 2, 3.
hide comments
smso:
2022-03-17 07:07:20
Testcases with 123 sequences of length=7
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Raghavendran Ramachandran:
2012-10-26 19:04:39
Interesting border cases. |
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Efim:
2011-07-12 22:30:55
Nice problem. |
Added by: | arun |
Date: | 2010-01-02 |
Time limit: | 0.202s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: NODEJS OBJC PERL6 SQLITE VB.NET |
Resource: | Kurukshetra OPC 2010 |