There are $n$ cities in Berland. Some pairs of cities are connected by roads. All roads are bidirectional. Each road connects two different cities. There is at most one road between a pair of cities. The cities are numbered from $1$ to $n$.

It is known that, from the capital (the city with the number $1$), you can reach any other city by moving along the roads.

The President of Berland plans to improve the country's road network. The budget is enough to repair exactly $n-1$ roads. The President plans to choose a set of $n-1$ roads such that:
 -  it is possible to travel from the capital to any other city along the $n-1$ chosen roads, -  if $d_i$ is the number of roads needed to travel from the capital to city $i$, moving only along the $n-1$ chosen roads, then $d_1 + d_2 + \dots + d_n$ is minimized (i.e. as minimal as possible). 
In other words, the set of $n-1$ roads should preserve the connectivity of the country, and the sum of distances from city $1$ to all cities should be minimized (where you can only use the $n-1$ chosen roads).

The president instructed the ministry to prepare $k$ possible options to choose $n-1$ roads so that both conditions above are met.

Write a program that will find $k$ possible ways to choose roads for repair. If there are fewer than $k$ ways, then the program should output all possible valid ways to choose roads.
The first line of the input contains integers $n$, $m$ and $k$ ($2 \le n \le 2\cdot10^5, n-1 \le m \le 2\cdot10^5, 1 \le k \le 2\cdot10^5$), where $n$ is the number of cities in the country, $m$ is the number of roads and $k$ is the number of options to choose a set of roads for repair. It is guaranteed that $m \cdot k \le 10^6$.

The following $m$ lines describe the roads, one road per line. Each line contains two integers $a_i$, $b_i$ ($1 \le a_i, b_i \le n$, $a_i \ne b_i$) — the numbers of the cities that the $i$-th road connects. There is at most one road between a pair of cities. The given set of roads is such that you can reach any city from the capital.
4 4 3
1 2
2 3
1 4
4 3
2
1110
1011
4 6 3
1 2
2 3
1 4
4 3
2 4
1 3
1
101001
5 6 2
1 2
1 3
2 4
2 5
3 4
3 5
2
111100
110110
2 1 200000
2 1
1
1
3 2 100000
1 2
2 3
1
11
3 2 100000
1 2
1 3
1
11
3 3 1000
1 2
2 3
3 1
1
101
5 6 166666
1 2
1 3
2 4
2 5
3 4
3 5
4
111100
110110
111001
110011
5 6 10
4 5
3 2
3 5
1 3
5 1
1 2
1
100111
6 9 10
3 5
3 2
1 3
2 1
6 3
1 6
4 2
1 5
6 5
1
001101110
10 14 100
2 8
4 7
1 4
9 1
6 9
8 6
10 2
8 4
1 7
6 5
10 9
3 10
6 2
1 3
6
10111001111001
00111011111001
00111001111011
10111001110101
00111011110101
00111001110111
15 20 100
6 7
15 11
2 15
9 5
9 1
8 2
2 10
2 12
3 11
5 12
14 9
4 11
11 2
13 5
12 7
6 1
13 3
8 6
10 8
3 7
4
10111100111101010111
10111100011111010111
10111100101101110111
10111100001111110111
16 20 100
9 12
7 1
9 6
1 5
5 14
9 11
6 1
3 1
1 16
5 6
11 3
9 5
10 7
13 1
4 3
5 16
9 8
15 13
9 2
14 3
4
11111011101011101110
11011011101111101110
11110011101011101111
11010011101111101111
16 20 100
8 4
2 16
8 7
6 11
8 9
10 4
1 4
3 9
5 8
3 14
5 6
11 4
10 15
1 16
9 5
13 10
5 14
3 1
12 16
6 1
2
11110111011011010111
11100111011111010111
16 20 100
7 8
6 5
15 1
7 2
2 12
1 7
7 9
13 15
11 14
3 10
8 3
2 14
3 4
1 5
4 15
10 12
11 4
4 8
7 16
14 13
8
11111111011101101010
11111111010111101010
11111111001101111010
11111111000111111010
11111111011001101011
11111111010011101011
11111111001001111011
11111111000011111011
16 20 100
6 3
15 16
14 2
15 5
6 12
13 16
9 12
16 3
5 11
16 14
10 8
4 3
2 7
8 14
2 3
1 3
13 15
14 3
3 5
8 2
4
11001111101111110110
11001111101110110111
10011111101111110110
10011111101110110111
16 20 100
4 6
7 15
10 5
8 6
9 11
12 15
14 1
13 7
12 2
4 12
14 16
3 16
9 15
4 5
8 15
6 3
2 11
9 12
5 15
3 11
6
11111011101111011001
11111011011111011001
11111011001111011101
11111011101101111001
11111011011101111001
11111011001101111101
18 23 100
5 13
10 2
6 3
8 2
1 16
18 10
12 1
2 1
18 2
6 2
4 1
16 7
15 18
17 11
9 17
17 3
16 15
12 14
14 17
5 9
9 2
17 13
7 10
4
11111011111101101101100
01111011111101101101110
11111011111101001111100
01111011111101001111110
18 23 100
12 14
2 11
1 13
2 7
18 17
16 13
9 13
15 1
9 12
3 4
10 11
18 4
2 18
13 8
5 6
9 2
9 4
13 5
5 15
15 4
18 1
10 9
16 5
4
11111111110111100100110
11111111110011100101110
11111111110111100010110
11111111110011100011110
18 23 100
14 1
4 3
2 9
16 10
10 12
10 1
6 15
1 8
3 12
11 14
9 8
15 1
15 9
7 10
1 5
18 16
3 1
8 14
4 9
11 13
13 6
10 17
13 15
4
11111111011101111000011
11111111010111111000011
11110111111101111000011
11110111110111111000011
18 23 100
5 13
6 7
8 2
13 7
18 12
11 18
9 5
5 4
17 15
11 4
6 13
13 15
18 16
14 15
4 8
7 2
12 14
12 1
2 10
13 4
8 5
3 18
1 10
4
01111110110011011110111
01111110100011111110111
01101110110111011110111
01101110100111111110111
18 23 100
4 16
12 17
2 12
16 13
5 8
2 18
5 15
11 5
15 11
13 9
10 4
15 10
13 7
14 15
4 9
5 1
6 13
3 17
18 11
15 3
9 5
1 9
3 5
4
11001111011011111110011
11001111010111111110011
01011111011011111110011
01011111010111111110011
50 70 10000
1 12
43 48
39 50
2 9
3 10
2 26
38 8
38 39
12 17
6 19
31 21
17 23
39 25
25 9
42 1
32 18
1 18
32 19
19 41
26 32
4 28
12 15
49 5
16 11
4 30
34 16
26 23
44 30
37 4
25 36
15 6
29 27
48 11
29 21
30 20
32 20
21 30
17 7
33 2
22 19
25 34
49 38
38 24
20 46
14 30
33 47
38 45
18 40
44 43
36 40
7 33
11 27
49 35
25 30
37 34
46 28
42 18
37 50
21 47
40 21
29 50
27 49
16 6
49 44
20 6
37 26
9 13
27 19
1 29
19 10
1536
1111111110111011111111111001001111011101001111110101101001101100001011
1111111110111011111111110001101111011101001111110101101001101100001011
1110111110111111111111111001001111011101001111110101101001101100001011
1110111110111111111111110001101111011101001111110101101001101100001011
1111111110111011111111101001001111011101001111110101101001101110001011
1111111110111011111111100001101111011101001111110101101001101110001011
1110111110111111111111101001001111011101001111110101101001101110001011
1...
11 18 55555
1 2
1 3
2 4
2 5
3 4
3 5
4 6
4 7
5 6
5 7
6 8
6 9
7 8
7 9
8 10
8 11
9 10
9 11
256
111100110011001100
110110110011001100
111001110011001100
110011110011001100
111100011011001100
110110011011001100
111001011011001100
110011011011001100
111100100111001100
110110100111001100
111001100111001100
110011100111001100
111100001111001100
110110001111001100
111001001111001100
110011001111001100
111100110001101100
110110110001101100
111001110001101100
110011110001101100
111100011001101100
110110011001101100
111001011001101100
110011011001101100
111100100101101100
110110...
17 30 33333
1 2
1 3
2 4
2 5
3 4
3 5
4 6
4 7
5 6
5 7
6 8
6 9
7 8
7 9
8 10
8 11
9 10
9 11
10 12
10 13
11 12
11 13
12 14
12 15
13 14
13 15
14 16
14 17
15 16
15 17
16384
111100110011001100110011001100
110110110011001100110011001100
111001110011001100110011001100
110011110011001100110011001100
111100011011001100110011001100
110110011011001100110011001100
111001011011001100110011001100
110011011011001100110011001100
111100100111001100110011001100
110110100111001100110011001100
111001100111001100110011001100
110011100111001100110011001100
111100001111001100110011001100
110110001111001100110011001100
111001001111001100110011001100
110011001111001100110011...
21 38 26315
1 2
1 3
2 4
2 5
3 4
3 5
4 6
4 7
5 6
5 7
6 8
6 9
7 8
7 9
8 10
8 11
9 10
9 11
10 12
10 13
11 12
11 13
12 14
12 15
13 14
13 15
14 16
14 17
15 16
15 17
16 18
16 19
17 18
17 19
18 20
18 21
19 20
19 21
26315
11110011001100110011001100110011001100
11011011001100110011001100110011001100
11100111001100110011001100110011001100
11001111001100110011001100110011001100
11110001101100110011001100110011001100
11011001101100110011001100110011001100
11100101101100110011001100110011001100
11001101101100110011001100110011001100
11110010011100110011001100110011001100
11011010011100110011001100110011001100
11100110011100110011001100110011001100
11001110011100110011001100110011001100
111100001111001100110011...
print("_RANDOM_GUESS_1689443185.9838364")# 1689443185.9838567