Juggling Letters

You are given n strings s_1, s_2, …, s_n consisting of lowercase Latin letters.

In one operation you can remove a character from a string s_i and insert it to an arbitrary position in a string s_j (j may be equal to i). You may perform this operation any number of times. Is it possible to make all n strings equal?

Input

The first line contains t (1 ≤ t ≤ 10): the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 1000): the number of strings.

n lines follow, the i-th line contains s_i (1 ≤ \lvert s_i \rvert ≤ 1000).

The sum of lengths of all strings in all test cases does not exceed 1000.

Output

If it is possible to make the strings equal, print "YES" (without quotes).

Otherwise, print "NO" (without quotes).

You can output each character in either lowercase or uppercase.

Example

Input

4 2 caa cbb 3 cba cba cbb 4 ccab cbac bca acbcc 4 acb caf c cbafc

Output

YES NO YES NO

Note

In the first test case, you can do the following:

• Remove the third character of the first string and insert it after the second character of the second string, making the two strings "ca" and "cbab" respectively.
• Remove the second character of the second string and insert it after the second character of the first string, making both strings equal to "cab".

In the second test case, it is impossible to make all n strings equal.

inputFormat

Input

The first line contains t (1 ≤ t ≤ 10): the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 1000): the number of strings.

n lines follow, the i-th line contains s_i (1 ≤ \lvert s_i \rvert ≤ 1000).

The sum of lengths of all strings in all test cases does not exceed 1000.

outputFormat

Output

If it is possible to make the strings equal, print "YES" (without quotes).

Otherwise, print "NO" (without quotes).

You can output each character in either lowercase or uppercase.

Example

Input

4 2 caa cbb 3 cba cba cbb 4 ccab cbac bca acbcc 4 acb caf c cbafc

Output

YES NO YES NO

Note

In the first test case, you can do the following:

• Remove the third character of the first string and insert it after the second character of the second string, making the two strings "ca" and "cbab" respectively.
• Remove the second character of the second string and insert it after the second character of the first string, making both strings equal to "cab".

In the second test case, it is impossible to make all n strings equal.

样例

4
2
caa
cbb
3
cba
cba
cbb
4
ccab
cbac
bca
acbcc
4
acb
caf
c
cbafc

YES
NO
YES
NO

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