H

War Map

The country you live in is actually a land of rivers. Almost every city of the country is surrounded by rivers. Fortunately there are many bridges in the country that connect the cities. Suddenly the country is under attack and the opposition is trying to destroy the bridges to isolate the cities. You, as a commander of a sector, now want to know the current status of the sector. The sector consists of N cities. You asked your assistant to collect the current connectivity information of the sector. But he could only manage to get di for each of the cities in the sector. Here di represents the number of different cities to which city i is directly connected. Note that a city is not considered to be connected with itself. Now, you want to draw a graph that is consistent with the information. You also want to give each of the cities a color such that directly connected cities do not have same color. But you have only two colors to use. You want to know whether such a graph can be drawn.

Input

Input starts with an integer T (≤ 500), denoting the number of test cases.

Each case starts with a line containing an integer N (2 ≤ N ≤ 20). The next line contains N integers di (0 ≤ di ≤ N).

Output

For each case, print the case number and 'YES' if it's possible to draw such a graph or 'NO' if it isn't.

Sample Input

Output for Sample Input

 
4
4
3 1 3 3
5
1 2 1 1 3
4
2 3 2 3
7
4 1 2 3 1 2 3
 
Case 1: NO
Case 2: YES
Case 3: NO
Case 4: YES

Notes

 

For case 2, you can draw the following graph

 

For case 3, you can draw the following graph, but using only two colors it can't be colored.

Problem Setter: Md. Towhidul Islam Talukder, Special Thanks: Jane Alam Jan