To open sesame one needs a set of tokens containing at least z gold tokens, s silver tokens and m copper tokens.

Initially, Ali Baba has at his disposal a certain number of tokens of each kind. He can exchange them with the Guardian of sesame, according to given rules.

Every rule is of the form:

z₁, s₁, m₁ -> z₂, s₂, m₂ (z_i, s_i, m_i are from the set {0,1,2,3,4}).

Such a rule denotes that Ali Baba can exchange z₁ gold tokens, s₁ silver tokens and m₁ copper tokens for z₂ gold tokens, s₂ silver tokens and m₂ copper tokens.

Tokens received in a transaction can be exchanged in the next transactions.

Task

• reads sets of data from the text file ALI.IN; each set of data contains:
  • the number of gold, silver and copper tokens owned by Ali Baba initially;
  • the description of the set of tokens needed to open sesame;
  • the rules of transactions;
• for each set of data, checks if there exists a finite sequence of transactions, after which Ali Baba can receive the set of tokens opening sesame and if so writes to the text file ALI.OUT the minimal length of such a sequence; if such a sequence does not exist writes to the same file the answer NIE (which means NO in Polish).

Input

Then the sets of data follow. Each set of data consists of many lines.

In the first line there are three non-negative integers z_p, s_p, m_p from the set {0,1,2,3,4}. They are the numbers of gold, silver and copper tokens respectively, owned by Ali Baba initially.

In the second line there are three integers z, s, m from the set {0,1,2,3,4}. They are the numbers of gold, silver and copper tokens needed to open sesame.

In the third line there is written the number of rules r, 1<=r<=10.

In each of the following r lines there is a sequence of six numbers z₁, s₁, m₁, z₂, s₂, m₂ from the set {0,1,2,3,4}. They describe a single rule: z₁, s₁, m₁ -> z₂, s₂, m₂.

The numbers in each line are separated by single spaces.

Output

• one non-negative integer, i.e. the minimal number of transactions that Ali Baba has to carry out in order to receive the set of tokens opening sesame,
• or the word NIE (which means NO in Polish).

Example
For the text file ALI.IN:

2
2 2 2
3 3 3
3
0 1 1 2 0 0
1 0 1 0 2 0
1 1 0 0 0 2
1 1 1
2 2 2
4
1 0 0 0 1 0
0 1 0 0 0 1
0 0 1 1 0 0
2 0 0 0 2 2

NIE
9