During the Samhan Period or the Proto-Three
Kingdoms Period, which refers to the period after
the fall of Gojoseon and before the maturation of
Goguryeo, Baekje, and Silla into full-fledged
kingdoms, the city-states of central and southern
Korean Peninsula were grouped into three
confederacies called Mahan, Jinhan, and Byeonhan.
Sam means three, and Han is a Korean word
meaning great or leader. The names of these
confederacies are reflected in the current name of
Korea, Daehan Minguk (literally, “Great Han
People's Nation”).

One of the city-states called Saro-guk, which was
established by King Park Hyeokgeose in 57 BCE,
around present-day Gyeongju, was the leader of
Jinhan confederacy. As the city-state expanded, it changed its name to Silla, which was the longest sustained
dynasty in Asian history. We knew little about other city-states of Jinhan confederacy, with the exception of
their names.

Recently, Prof. Choi, who is a highly considered archaeologist, announced that he had found the tomb of King
Park Hyeokgeose. By virtue of his major archaeological discovery, we get to know a little of the daily life of
Jinhan people. However, even the locations of city-states of Jinhan confederacy except for Saro-guk have
been not known as yet. Thanks to his success of deciphering the inscription engraved on the stone wall of the
tomb, the distances between some pairs of city-states of Jinhan confederacy including pairs between Saro-guk
and every other city-state have been known.

An ambitious research for estimating the locations of all city-states of Jinhan confederacy is initiated by Prof.
Choi and his research group. He conjectures that the city-states of Jinhan confederacy were located in a row.
His conjecture is based on the knowledge that Jinhan confederacy was located at between the Taebaek
Mountains and East Sea. To verify his conjecture, he develops a mathematical model, where the area occupied
by Jinhan confederacy is simplified into a straight line, say the x-axis, and the distance between two city-
states is represented by a positive integer. The location of a city-state can be described by a point on the x-axis. It is assumed that Saro-guk is located at the origin of the x-axis.

Prof. Choi wants to determine whether or not it is possible to locate all the city-states of Jinhan confederacy
on the x-axis subject to the distance constraints between the city-states. Of course, no two city-states should
occupy the same location. Write a program that can help him. We denote by n the number of city-states of
Jinhan confederacy, and assume that the city-states are numbered from 1 to n inclusive and thus no two city-
states have the same number. Saro-guk has a number of
1. The distances between some pairs of city-states
including pairs of Saro-guk and every other city-state are given as input.

For example, if n is equal to three, the distance between city-states numbered 1 and 2 is four, and the
distance between city-states 1 and 3 is also four, then it is possible to locate the city-states 1, 2, and 3 at positions 0, 4, and -4 on the x-axis, respectively. They can be located at positions 0, -4, and 4, too.
However, they cannot be located neither at positions 0, 4, and
4 nor at positions 0, -4, and -4.

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