Zig-zag P71711

Statement

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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