Problem #2206 - ECNU Online Judge

单点时限: 2.0 sec

内存限制: 256 MB

There are $n$ towns with their own airports in the country X. We know the maximal capacities of the airports - the airport in the town $M_{i}$ can have at most $d_{i}$ connections with other towns. The task is to design the net of air connections among the towns in such a way that the town $M_{i}$ has exactly $d_{i}$ connections with other towns. We assume that connections are two-way and that each pair of towns has at most one connection between them.

Write a program that:

reads the number of towns $n$ and the numbers $d_{i}$ ,
designs the net of air connections in such a way that for every $i$ , $1 \leq i \leq n$ , the town $M_{i}$ has exactly $d_{i}$ connections with other towns,
writes the list of all connections.

We assume that for the given data a solution exists. If there exists more than one solution the program should find only one.

输入格式

In the first line there is written one integer $n$ , $3 \leq n \leq 500$ , which is the number of towns.

In the following $n$ lines there are written positive integers $d_{i}$ (one integer in each line).

输出格式

Your program should write all the connections of the created net. The description of each connection consists of two positive integers separated by a single space. These integers are the numbers of two connected towns. Each description should be placed in a separate line. The numbers of towns in a line can be written in an arbitrary order. Similarly, the order of connections is not important.

样例

Input

Output

5 人解决，13 人已尝试。

6 份提交通过，共有 46 份提交。

8.3 EMB 奖励。

创建: 16 年，9 月前.

修改: 7 年，3 月前.

最后提交: 4 年，5 月前.

来源: POI 1997 II Stage

construction

2206. Airports

输入格式

输出格式

样例

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