Problem 1375 - USTC Online Judge

Rank

Problem 1375

Restoring Table

Time Limit: 1000ms
Memory Limit: 65536kb

Description

Recently Polycarpus has learned the "bitwise AND" operation (which is also called "AND") of non-negative integers. Now he wants to demonstrate the school IT teacher his superb manipulation with the learned operation.

For that Polycarpus came to school a little earlier and wrote on the board a sequence of non-negative integers a₁, a₂, ..., a_n. He also wrote a square matrix b of size n × n. The element of matrix b that sits in the i-th row in the j-th column (we'll denote it as b_ij) equals:

the "bitwise AND" of numbers a_i and a_j (that is, b_ij = a_i & a_j), if i ≠ j;
-1, if i = j.

Having written out matrix b, Polycarpus got very happy and wiped a off the blackboard. But the thing is, the teacher will want this sequence to check whether Polycarpus' calculations were correct. Polycarus urgently needs to restore the removed sequence of integers, or else he won't prove that he can count correctly.

Help Polycarpus, given matrix b, restore the sequence of numbers a₁, a₂, ..., a_n, that he has removed from the board. Polycarpus doesn't like large numbers, so any number in the restored sequence mustn't exceed 10⁹.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the size of square matrix b. Next n lines contain matrix b. The i-th of these lines contains n space-separated integers: the j-th number represents the element of matrix b_ij. It is guaranteed, that for all i (1 ≤ i ≤ n)the following condition fulfills: b_ii = -1. It is guaranteed that for all i, j (1 ≤ i, j ≤ n; i ≠ j) the following condition fulfills: 0 ≤ b_ij ≤ 10⁹, b_ij = b_ji.

Output

Print n non-negative integers a₁, a₂, ..., a_n (0 ≤ a_i ≤ 10⁹) — the sequence that Polycarpus wiped off the board. Separate the numbers by whitespaces.

It is guaranteed that there is sequence a that satisfies the problem conditions. If there are multiple such sequences, you should print the one which has minimum sum.

Sample Input

4
-1 128 128 128
128 -1 148 160
128 148 -1 128
128 160 128 -1
4
-1 128 128 128
128 -1 148 160
128 148 -1 128
128 160 128 -1

Sample Output

128 180 148 160
128 180 148 160

Hint

思考：对于给定的矩阵b，其对应的数字序列是唯一的么？如果不唯一，那怎样找出所有解呢？
注意：有多个输入实例。

Source

CodeForces 245D

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