Write a program that reads several matrices of integer numbers, and that for each one tells whether the result of traversing it in zig-zags is a strictly increasing sequence. We must start at the top-left position, go down the first column, up the second column, down the third column, and so on.

Input

Input consists of several matrices, each with the number of rows r ≥ 1 and the number of columns c ≥ 1, followed by r rows with c integer numbers each.

Output

For every matrix, print its number followed by either “yes” o “no”, depending on whether the zig-zag traversal of the matrix generates a strictly increasing sequence or not.

Public test cases

**Input**

3 4 10 15 36 41 11 14 37 40 12 13 38 39 3 2 10 11 12 13 14 15 2 2 5 7 6 6 2 3 1 4 5 2 3 5 1 1 -3 1 3 4 6 8 2 1 100 200

**Output**

matriu 1: yes matriu 2: no matriu 3: no matriu 4: no matriu 5: yes matriu 6: yes matriu 7: yes

Information

- Author
- Professors de P1
- Language
- English
- Translator
- Salvador Roura
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++ Java Python
- User solutions
- C++ Python