Problem I: Mobile Network

The trafic on the Internet is increasing these days due to smartphones. The wireless carriers have to enhance their network infrastructure.

The network of a wireless carrier consists of a number of base stations and lines. Each line connects two base stations bi-directionally. The bandwidth of a line increases every year and is given by a polynomial f(x) of the year x.

Your task is, given the network structure, to write a program to calculate the maximal bandwidth between the 1-st and N-th base stations as a polynomial of x.

Input

The input consists of multiple datasets. Each dataset has the following format:

N M
u₁ v₁ p₁
...
u_M v_M p_M

The first line of each dataset contains two integers N (2 ≤ N ≤ 50) and M (0 ≤ M ≤ 500), which indicates the number of base stations and lines respectively. The following M lines describe the network structure. The i-th of them corresponds to the i-th network line and contains two integers u_i and v_i and a polynomial p_i. u_i and v_i indicate the indices of base stations (1 ≤ u_i, v_i ≤ N); p_i indicates the network bandwidth.

Each polynomial has the form of:

a_Lx^L + a_L-1x^L-1 + ... + a₂x² + a₁x + a₀

where L (0 ≤ L ≤ 50) is the degree and a_i's (0 ≤ i ≤ L, 0 ≤ a_i ≤ 100) are the coefficients. In the input,

• each term a_ixⁱ (for i ≥ 2) is represented as <a_i>x^<i>
• the linear term (a₁x) is represented as <a₁>x;
• the constant (a₀) is represented just by digits;
• these terms are given in the strictly decreasing order of the degrees and connected by a plus sign ("+");
• just like the standard notations, the <a_i> is omitted if a_i = 1 for non-constant terms;
• similarly, the entire term is omitted if a_i = 0 for any terms; and
• the polynomial representations contain no space or characters other than digits, "x", "^", and "+".

For example, 2x² + 3x + 5 is represented as 2x^2+3x+5; 2x³ + x is represented as 2x^3+x, not 2x^3+0x^2+1x+0 or the like. No polynomial is a constant zero, i.e. the one with all the coefficients being zero.

The end of input is indicated by a line with two zeros. This line is not part of any dataset.

Output

For each dataset, print the maximal bandwidth as a polynomial of x. The polynomial should be represented in the same way as the input format except that a constant zero is possible and should be represented by "0" (without quotes).

Sample Input

3 3
1 2 x+2
2 3 2x+1
3 1 x+1
2 0
3 2
1 2 x
2 3 2
4 3
1 2 x^3+2x^2+3x+4
2 3 x^2+2x+3
3 4 x+2
0 0

Output for the Sample Input

2x+3
0
2
x+2

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