Two neighbours, Alan and Bob, live in the city, where there are three buildings only: a cinema, a shop and the house, where they live. The rest is a big asphalt square. 

Once they went to the cinema, and the film impressed them so deeply, that when they left the cinema, they did not want to stop discussing it.

Bob wants to get home, but Alan has to go to the shop first, and only then go home. So, they agreed to cover some distance together discussing the film (their common path might pass through the shop, or they might walk circles around the cinema together), and then to part each other's company and go each his own way. After they part, they will start thinking about their daily pursuits; and even if they meet again, they won't be able to go on with the discussion. Thus, Bob's path will be a continuous curve, having the cinema and the house as its ends. Alan's path — a continuous curve, going through the shop, and having the cinema and the house as its ends.

The film ended late, that's why the whole distance covered by Alan should not differ from the shortest one by more than *t*<sub class="lower-index">1</sub>, and the distance covered by Bob should not differ from the shortest one by more than *t*<sub class="lower-index">2</sub>.

Find the maximum distance that Alan and Bob will cover together, discussing the film.
The first line contains two integers: *t*<sub class="lower-index">1</sub>, *t*<sub class="lower-index">2</sub> (0 ≤ *t*<sub class="lower-index">1</sub>, *t*<sub class="lower-index">2</sub> ≤ 100). The second line contains the cinema's coordinates, the third one — the house's, and the last line — the shop's. 

All the coordinates are given in meters, are integer, and do not exceed 100 in absolute magnitude. No two given places are in the same building.
none
0 2
0 0
4 0
-3 0
1.0000000000
0 0
0 0
2 0
1 0
2.0000000000
0 2
0 0
40 0
-31 1
1.0002538218
100 2
0 0
4 0
-3 0
6.0000000000
2 100
0 0
4 0
-3 0
12.0000000000
0 0
0 0
5 0
10 0
5.0000000000
2 0
0 0
5 0
10 0
5.0000000000
0 2
0 0
5 0
10 0
6.0000000000
0 0
0 0
4 0
4 3
0.0000299999
0 4
0 0
4 0
4 3
8.0000000000
0 3
0 0
4 0
4 3
4.3421111488
1 4
0 0
4 0
4 3
8.0000000000
0 0
0 0
100 100
100 0
0.0000241421
1 1
0 0
100 100
100 0
11.8620549792
0 0
0 0
-1 -1
1 -1
0.0000099999
0 0
1 2
1 -2
1 1
4.0000000000
2 1
1 3
0 1
0 0
3.2360679775
1 1
1 1
-1 -4
4 -3
3.4140469620
2 4
3 1
-5 -1
2 2
11.0299866682
1 1
5 5
8 -1
-3 -3
3.4363113325
0 8
13 -2
15 -16
4 9
4.2383217359
4 12
1 -3
-21 -29
30 10
8.8182331094
25 22
22 -21
14 -25
8 21
26.9132525667
10 20
-2 -18
30 26
-14 38
47.7344371741
12 3
9 7
-26 -30
-27 33
19.0794600792
31 21
-42 42
-2 10
33 -40
72.2249938995
23 68
60 -68
-70 13
-50 26
191.5464988652
29 26
-33 2
15 -42
-52 48
28.8420189634
4 5
-84 52
-20 -39
51 91
20.5654840916
43 30
88 45
-41 -76
-26 -46
206.8671818060
2 32
-91 -7
-69 -99
3 -7
42.1044438082
28 0
-98 -73
45 -19
-82 -60
33.3590240317
7 69
75 -97
34 89
-21 19
246.5947108716
1 45
-52 36
-86 7
46 80
23.6287723817
36 7
64 -16
18 -95
50 46
26.4522291627
0 5
3 9
-7 -10
-9 -10
24.4722050542
1 0
4 4
6 1
6 -10
3.6055512755
2 6
77 86
-48 -76
-65 28
68.8370182423
32 8
-74 -85
69 -13
-59 64
80.9525769682
7 0
2 3
-3 -8
7 -9
10.3637557241
3 0
3 0
-10 -5
-8 10
4.3880652624
48 3
-17 -70
20 91
-92 -100
34.1872425101
24 3
-86 1
3 70
-71 -85
21.3881481586
0 11
7 -11
0 19
-13 -16
9.4432695006
38 5
-99 16
91 45
22 -70
105.0959316870
5 0
75 -56
-12 24
99 19
8.0208146392
39 0
-7 -57
52 -77
24 -98
57.7524735602
0 5
-20 -2
16 -6
16 -2
40.0000000000
26 6
98 -44
60 67
-41 -15
64.2681170638
13 5
-95 7
-39 81
65 -47
34.7382933870
5 0
-20 -13
-9 -5
10 -13
13.6014705087
5 0
8 -19
-6 -12
-15 -14
15.6524758425
10 1
-71 23
51 92
-72 10
7.4826465918
4 0
8 -4
7 7
-6 9
9.4951445784
45 0
85 34
-21 -47
28 44
56.8197308538
5 0
14 17
20 5
17 -20
13.4164078650
80 3
35 -55
-36 -53
-96 -53
74.0281634283
3 4
-80 -78
23 -81
-49 -50
27.3700259542
82 92
-85 44
19 -65
-47 -1
232.8329767670
1 65
-56 -85
7 34
-38 68
148.7518367529
83 99
53 100
-74 -28
-29 32
264.5269918847
65 12
41 38
5 4
-96 -53
61.5176736126
95 75
-99 -26
55 -1
72 17
231.0160248180
68 11
-85 65
-70 61
38 12
26.5241746963
18 26
68 67
-46 -36
-46 95
84.4001524822
72 52
-47 -88
33 1
88 51
171.6703806295
39 99
-93 -91
66 -6
87 -12
257.4134712717
38 23
2 45
49 2
87 -69
86.7024332345
83 0
94 -62
0 -34
-87 49
98.0815986819
16 68
31 -70
10 17
4 30
133.8987073310
67 10
92 -2
-58 -79
70 86
61.1979627104
49 9
-91 -29
-54 -72
73 6
65.7274184147
48 59
-16 -32
-64 76
-26 49
176.2303976942
85 4
94 100
-16 40
45 -26
129.2996408614
0 2
0 0
40 0
-31 0
1.0000000000
print("_RANDOM_GUESS_1689418972.1949453")# 1689418972.1949642