CF173D.Deputies

The Trinitarian kingdom has exactly n = 3_k_ cities. All of them are located on the shores of river Trissisipi, which flows through the whole kingdom. Some of the cities are located on one side of the river, and all the rest are on the other side.

Some cities are connected by bridges built between them. Each bridge connects two cities that are located on the opposite sides of the river. Between any two cities exists no more than one bridge.

The recently inaugurated King Tristan the Third is busy distributing his deputies among cities. In total there are k deputies and the king wants to commission each of them to control exactly three cities. However, no deputy can be entrusted to manage the cities, which are connected by a bridge — the deputy can set a too high fee for travelling over the bridge to benefit his pocket, which is bad for the reputation of the king.

Help King Tristan the Third distribute the deputies between the cities, if it is possible.

三一王国恰好有 $ n = 3k $ 座城市。所有城市均位于贯穿整个王国的特里西西皮河（Trissisipi River）沿岸。其中一部分城市位于河流的一侧，其余所有城市则位于另一侧。

某些城市之间通过桥梁相互连接。每座桥梁连接位于河流对岸的两座城市。任意两座城市之间至多存在一座桥梁。

新近登基的三世国王特里斯坦（Tristan the Third）正忙于将他的 $ k $ 名副手分配到各城市中。国王希望每位副手恰好管辖三座城市。然而，任何一位副手都不得被委派去管理由桥梁直接相连的两座城市——否则该副手可能为牟取私利而对过桥通行收取过高费用，从而损害国王的声誉。

若可行，请帮助三世国王特里斯坦将副手们分配到各城市中。

The first line contains two integers n and m — the number of cities and bridges (3 ≤ n < 105, n = 3_k_, 0 ≤ m ≤ 105). Next m lines describe the bridges. The i-th line contains two integers a__i and b__i — the numbers of cities that are connected by the i-th bridge (1 ≤ a__i, b__i ≤ n, a__i ≠ b__i, 1 ≤ i ≤ m).

It is guaranteed that no bridge connects a city with itself and that any two cities are connected with no more than one bridge.

第一行包含两个整数 $n$ 和 $m$ —— 城市的数量与桥梁的数量（$3 \leq n < 10^5$，$n = 3k$，$0 \leq m \leq 10^5$）。接下来的 $m$ 行描述桥梁。第 $i$ 行包含两个整数 $a_i$ 和 $b_i$ —— 表示第 $i$ 座桥梁所连接的两座城市的编号（$1 \leq a_i, b_i \leq n$，$a_i \neq b_i$，$1 \leq i \leq m$）。

保证不存在连接城市自身的桥梁，且任意两座城市之间至多只有一座桥梁。

If distributing the deputies in the required manner is impossible, print in a single line "NO" (without the quotes).

Otherwise, in the first line print "YES" (without the quotes), and in the second line print which deputy should be put in charge of each city. The i-th number should represent the number of the deputy (from 1 to k), who should be in charge of city numbered i-th in the input — overall there should be n numbers.

If there are multiple solutions, print any of them.

如果无法按要求分配代表，请在一行中输出 "NO"（不带引号）。

否则，第一行输出 "YES"（不带引号），第二行输出每个城市应由哪位代表负责。其中第 $i$ 个数字表示应负责输入中第 $i$ 个城市的代表编号（从 $1$ 到 $k$）——总共应有 $n$ 个数字。

若存在多种解法，输出任意一种即可。