# Reactor Cooling

A group of young scientists in a developing country has decided to construct a nuclear reactor to produce enriched plutonium. As the computer expert in this team, your role is to design the reactor's cooling system.

The cooling system is comprised of a network of pipes connecting various nodes. Liquid flows through these pipes, and each pipe has a predetermined flow direction. The nodes in the cooling system are numbered from 1 to N. The system must be configured so that, for every node, the volume of liquid entering the node per unit time is equal to the volume exiting it. Specifically, if f_ij units of liquid flow from node i to node j per unit time (with f_ij = 0 if there is no pipe from i to j), then for each node i, the following condition must be satisfied:

Each pipe has a capacity c_ij. Additionally, to ensure adequate cooling, at least l_ij units of liquid must flow through each pipe per unit time. Therefore, for the pipe from node i to node j, it must hold that l_ij ≤ f_ij ≤ c_ij.

You are provided with a description of the cooling system. Your task is to determine how the liquid can be directed through the pipes to meet all the specified conditions.

## Input

The first line of the input file contains the numbers N and M – the number of nodes and pipes (1 ≤ N ≤ 200). The following M lines describe the pipes. Each line contains four integers i, j, l_ij, and c_ij. Any two nodes are connected by at most one pipe; if there is a pipe from i to j, there is no pipe from j to i, and no node is connected to itself by a pipe. The constraints are 0 ≤ l_{ij }≤ c_{ij }≤ 10^5.

## Output

If a solution exists, output the word YES on the first line of the output file. Then, output M numbers representing the amount of liquid that should flow through each pipe, in the order the pipes are listed in the input file. If no solution exists, output NO.