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time limit per test: 0.25 sec.

memory limit per test: 4096 KB

memory limit per test: 4096 KB

input: standard

output: standard

output: standard

A head of a rich company decided that the company needs to have its own basketball team in the NBA. He thinks that a team will be successful only if the heights of players don't differ from 2000 mm too much. He took on a coach and this coach selected N players. The height of each player was in range of 1950..2050 millimeters and their average height was exactly 2000 mm. Moreover, the height of each player was integer number of micrometers (micrometer is 1e-6 meters).

Now the head of that company wants to see his new team. He wants to check, if his will is done, but he is going to check it in quite a strange way. The players stands in a line in some order, then the head selects two players and counts the summary height H of these two players and players who are between them, and the number of these players K. If this sum H differs from 2000*K mm more than on 10 cm, then he says that the team is bad. Of course, the coach doesn't want his team to be named "bad", and he don't know, what players will be selected by the head. So he asks you to help him.

Write a program that will find the order of players in line, so that the head of a company will not say the team is bad.

Now the head of that company wants to see his new team. He wants to check, if his will is done, but he is going to check it in quite a strange way. The players stands in a line in some order, then the head selects two players and counts the summary height H of these two players and players who are between them, and the number of these players K. If this sum H differs from 2000*K mm more than on 10 cm, then he says that the team is bad. Of course, the coach doesn't want his team to be named "bad", and he don't know, what players will be selected by the head. So he asks you to help him.

Write a program that will find the order of players in line, so that the head of a company will not say the team is bad.

On the first line of input there is one integer N (1<=N<=6000) --- the number of players selected into a team (these are the base players and substitutions and so on). Then N real numbers follow --- the heights of the players in meters.

If the solution exists, write on the first line of the output one word "yes" (without quotes). On the second line write the order of players in which they must stand in line. The players are numbered starting from 1 in that order how their heights are written in input. If several solutions exist, output any. If there exist no solution, write on the first line of output only one word "no" (without quotes).

Input

6

1.95 1.95 1.96 2.04 2.05 2.05

1.95 1.95 1.96 2.04 2.05 2.05

Output

yes

1 6 2 5 3 4

1 6 2 5 3 4

Author: | Nizhny Novgorod city mathematic olympiad jury |

Resource: | Nizhny Novgorod city mathematic olympiad, 8th form |

Date: | 21.12.2002 |

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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