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题目描述

A robot is designed to move on a map from South toward North. When some obstacle is encountered, the robot can only turn toward West and moves until it can turn toward North and continue.

Given a squared map with $n\times n$ blocks, a robot can start from any position below the bottom line (South) and its target is to reach the top line (North). (By the way, kindly remind you that the left-hand-side of the map is West and the right-hand-side is East.)

If some obstacles are placed in the map, the robot might get trapped if it starts from certain positions and can never reach the North line. For example, in the situation given by the following figure, the robot will be trapped if it starts from either position 7 or 8.

Your job is to point out those starting positions which will get the robot trapped.

Note: it is assumed that a robot can move out of the map boundary, and all the blocks around the map are open, without any obstacle. Hence if the robot starts from any position out of the West or East boundary, it can certainly reach North without any problem. Therefore we only have to consider the positions between the West and East boundaries (e.g. the positions from 1 to 10 below the South line in the above figure). Besides, as long as the robot can reach the North line, it is considered successful even of it ends up at out of the boundary (e.g. the robot will have to move out of the map if starts from either the positions 1 or 2, but it can still reach the North line).

输入格式

Each input file contains one test case. Each case starts from a positive integer $n$ ($\le 100$) in a line, which is the size of the map. Then $n$ lines follow, each contains $n$ characters, which are either 0 for an open block, or 1 for a block with obstacle. The first line corresponds to the North boundary and the last line the South.

输出格式

Output in a line all the starting positions which can get the robot trapped, in increasing order. The positions are indexed from West to East, starting from 1. It is guaranteed that there is at least one output. All the numbers must be separated by 1 space, and there must be no extra space at the beginning or the end of the line.

样例

10
0000000000
0000111010
1100100011
0000110001
0000000011
0000000000
0100000100
0001000000
0001000000
0001100000

7 8

限制

对于所有的测试用例,限制为400ms, 64MB