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문제

은하계의 충돌이 다가오고 있다.

미스테리한 MdI가 다스리는 은하계는 지금 우리 은하를 무력으로 합병하려고 하고 있다. 하지만 은하계 정부는 상황을 반전시킬 계획을 가지고 있다. 

우리 정보국은 적의 본부에 잠입했고, 놀라운 지능을 얻게되었다. 적은 정해진 계획에 의해서 병력을 움직인다. 그 계획은 각 요새에 주둔하고 있는 병력의 일정 비율이 다른 요새로 매 시간마다 이동하는 것이다. (요새 사이를 이동하는 시간은 무시할 수 있다)

자 이제 정부는 공격할 날짜를 정했다. 이제 적의 약점을 찾아야 한다. 하지만, 적의 은하는 매우 멀기 때문에 그 곳으로 날아가는데 1시간이 걸린다. 게다가 우리는 MdI가 우리의 목표를 알아채고 우리의 공격지점으로 갈 수 있는 모든 병력의 이동을 즉시 시작할 것을 알고 있다. (이 경우에는 방향에 상관 없이 이동 가능) 스파이는 당신에게 힘의 통계값을 알려 주었다.

입력

첫째 줄에 테스트 케이스의 개수 1 ≤ T ≤ 10가 주어진다. 각 테스트 케이스의 첫째 줄에는 적의 요새의 수 N (1 ≤ N ≤ 100)과 연결된 링크의 수 l (0 ≤ l ≤ (N - 1)2), 그리고 공격할 시간 t (0 ≤ t ≤ 5000)가 주어진다. 둘째 줄에는 N개의 double값 ui 가 주어진다. (0 ≤ ui ≤ 1000) ui는 각 요새에 있는 부대의 힘의 통계값이다. 다음 l개 줄에는 링크의 정보가 포함되어 있다. 각 링크의 정보의 첫 두 정수 sj (0 ≤ sj < N)와 tj (0 ≤ tj < N)는 링크의 출발장소와 도착장소이고, 다음에 주어지는 pj (0 < pj ≤ 1)는 sj에서 tj로 이동하는 병력의 비율이다.

출력

적의 은하에서 가장 약한 지점 (모일 수 있는 부대의 힘의 통계값이 가장 작은 곳)의 힘의 통계값을 출력한다. 소수점 오차는 10-6까지 허용한다.

예제 입력 1

3
4 3 1
100 200 10 305
0 1 0.25
1 2 0.1
2 0 0.75
4 3 1
100 200 10 312
0 1 0.25
1 2 0.1
2 0 0.75
4 4 5
100 200 300 400
0 1 0.2
1 2 0.2
2 3 0.3
3 0 0.2

예제 출력 1

305.000000000
310.000000000
659.879000000

힌트

그림 3 – 첫 번째 예제의 힘의 통계값 (왼쪽: 처음, 오른쪽: 1시간이 지난 후)

그림 4 – 공격을 시작한 시점에서 각 요새의 힘의 통계값 (이때, 링크는 양방향이 된다)

[{"problem_id":"9211","problem_lang":"0","title":"\ud0c0\uc774\ubc0d","description":"<p>\uc740\ud558\uacc4\uc758 \ucda9\ub3cc\uc774 \ub2e4\uac00\uc624\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ubbf8\uc2a4\ud14c\ub9ac\ud55c MdI\uac00 \ub2e4\uc2a4\ub9ac\ub294 \uc740\ud558\uacc4\ub294 \uc9c0\uae08 \uc6b0\ub9ac \uc740\ud558\ub97c \ubb34\ub825\uc73c\ub85c \ud569\ubcd1\ud558\ub824\uace0 \ud558\uace0 \uc788\ub2e4. \ud558\uc9c0\ub9cc \uc740\ud558\uacc4 \uc815\ubd80\ub294 \uc0c1\ud669\uc744 \ubc18\uc804\uc2dc\ud0ac \uacc4\ud68d\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc6b0\ub9ac \uc815\ubcf4\uad6d\uc740 \uc801\uc758 \ubcf8\ubd80\uc5d0 \uc7a0\uc785\ud588\uace0, \ub180\ub77c\uc6b4 \uc9c0\ub2a5\uc744 \uc5bb\uac8c\ub418\uc5c8\ub2e4. \uc801\uc740 \uc815\ud574\uc9c4 \uacc4\ud68d\uc5d0 \uc758\ud574\uc11c \ubcd1\ub825\uc744&nbsp;\uc6c0\uc9c1\uc778\ub2e4. \uadf8 \uacc4\ud68d\uc740 \uac01 \uc694\uc0c8\uc5d0 \uc8fc\ub454\ud558\uace0 \uc788\ub294 \ubcd1\ub825\uc758 \uc77c\uc815 \ube44\uc728\uc774 \ub2e4\ub978 \uc694\uc0c8\ub85c \ub9e4 \uc2dc\uac04\ub9c8\ub2e4 \uc774\ub3d9\ud558\ub294 \uac83\uc774\ub2e4. (\uc694\uc0c8 \uc0ac\uc774\ub97c \uc774\ub3d9\ud558\ub294 \uc2dc\uac04\uc740 \ubb34\uc2dc\ud560 \uc218 \uc788\ub2e4)<\/p>\r\n\r\n<p>\uc790 \uc774\uc81c \uc815\ubd80\ub294 \uacf5\uaca9\ud560 \ub0a0\uc9dc\ub97c \uc815\ud588\ub2e4. \uc774\uc81c \uc801\uc758 \uc57d\uc810\uc744 \ucc3e\uc544\uc57c \ud55c\ub2e4. \ud558\uc9c0\ub9cc, \uc801\uc758 \uc740\ud558\ub294 \ub9e4\uc6b0 \uba40\uae30 \ub54c\ubb38\uc5d0 \uadf8 \uacf3\uc73c\ub85c \ub0a0\uc544\uac00\ub294\ub370 1\uc2dc\uac04\uc774 \uac78\ub9b0\ub2e4. \uac8c\ub2e4\uac00 \uc6b0\ub9ac\ub294 MdI\uac00 \uc6b0\ub9ac\uc758 \ubaa9\ud45c\ub97c \uc54c\uc544\ucc44\uace0 \uc6b0\ub9ac\uc758 \uacf5\uaca9\uc9c0\uc810\uc73c\ub85c \uac08 \uc218 \uc788\ub294 \ubaa8\ub4e0 \ubcd1\ub825\uc758 \uc774\ub3d9\uc744 \uc989\uc2dc \uc2dc\uc791\ud560 \uac83\uc744 \uc54c\uace0 \uc788\ub2e4. (\uc774 \uacbd\uc6b0\uc5d0\ub294 \ubc29\ud5a5\uc5d0 \uc0c1\uad00 \uc5c6\uc774 \uc774\ub3d9 \uac00\ub2a5) \uc2a4\ud30c\uc774\ub294 \ub2f9\uc2e0\uc5d0\uac8c \ud798\uc758 \ud1b5\uacc4\uac12\uc744 \uc54c\ub824 \uc8fc\uc5c8\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 1 &le; T &le; 10\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uc801\uc758 \uc694\uc0c8\uc758 \uc218 N (1 &le; N &le; 100)\uacfc \uc5f0\uacb0\ub41c \ub9c1\ud06c\uc758 \uc218 l (0 &le; l &le; (N - 1)<sup>2<\/sup>), \uadf8\ub9ac\uace0 \uacf5\uaca9\ud560 \uc2dc\uac04 t (0 &le; t &le; 5000)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 N\uac1c\uc758 double\uac12 u<sub>i<\/sub> \uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; u<sub>i<\/sub> &le; 1000) u<sub>i<\/sub>\ub294 \uac01 \uc694\uc0c8\uc5d0 \uc788\ub294 \ubd80\ub300\uc758 \ud798\uc758 \ud1b5\uacc4\uac12\uc774\ub2e4. \ub2e4\uc74c l\uac1c \uc904\uc5d0\ub294 \ub9c1\ud06c\uc758 \uc815\ubcf4\uac00 \ud3ec\ud568\ub418\uc5b4 \uc788\ub2e4. \uac01 \ub9c1\ud06c\uc758 \uc815\ubcf4\uc758 \uccab \ub450 \uc815\uc218 s<sub>j<\/sub> (0 &le; s<sub>j<\/sub> &lt; N)\uc640 t<sub>j<\/sub> (0 &le; t<sub>j<\/sub> &lt; N)\ub294 \ub9c1\ud06c\uc758 \ucd9c\ubc1c\uc7a5\uc18c\uc640 \ub3c4\ucc29\uc7a5\uc18c\uc774\uace0, \ub2e4\uc74c\uc5d0 \uc8fc\uc5b4\uc9c0\ub294 p<sub>j<\/sub> (0 &lt; p<sub>j<\/sub> &le; 1)\ub294 s<sub>j<\/sub>\uc5d0\uc11c t<sub>j<\/sub>\ub85c \uc774\ub3d9\ud558\ub294 \ubcd1\ub825\uc758 \ube44\uc728\uc774\ub2e4.<\/p>\r\n","output":"<p>\uc801\uc758 \uc740\ud558\uc5d0\uc11c \uac00\uc7a5 \uc57d\ud55c \uc9c0\uc810 (\ubaa8\uc77c \uc218 \uc788\ub294 \ubd80\ub300\uc758 \ud798\uc758 \ud1b5\uacc4\uac12\uc774 \uac00\uc7a5 \uc791\uc740 \uacf3)\uc758 \ud798\uc758 \ud1b5\uacc4\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc18c\uc218\uc810 \uc624\ucc28\ub294 10<sup>-6<\/sup>\uae4c\uc9c0 \ud5c8\uc6a9\ud55c\ub2e4.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/timing1(1).png\" style=\"height:130px; width:530px\" \/><\/p>\r\n\r\n<p><strong>\uadf8\ub9bc 3<\/strong>&nbsp;&ndash; \uccab \ubc88\uc9f8 \uc608\uc81c\uc758 \ud798\uc758 \ud1b5\uacc4\uac12 (\uc67c\ucabd: \ucc98\uc74c, \uc624\ub978\ucabd: 1\uc2dc\uac04\uc774 \uc9c0\ub09c \ud6c4)<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/timing2.png\" style=\"height:133px; opacity:0.9; width:496px\" \/><\/p>\r\n\r\n<p><strong>\uadf8\ub9bc 4<\/strong>&nbsp;&ndash; \uacf5\uaca9\uc744 \uc2dc\uc791\ud55c \uc2dc\uc810\uc5d0\uc11c \uac01 \uc694\uc0c8\uc758 \ud798\uc758 \ud1b5\uacc4\uac12 (\uc774\ub54c, \ub9c1\ud06c\ub294 \uc591\ubc29\ud5a5\uc774 \ub41c\ub2e4)<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"9211","problem_lang":"1","title":"Timing","description":"<p>A clash of galaxies is coming!<\/p>\r\n\r\n<p>A galaxy ruled by the mysterious MdI is trying to annex our milky way, but the galactical government has plans to turn things round.<\/p>\r\n\r\n<p>Our intelligence agency has infiltrated the enemy&rsquo;s headquarter and gained surprising intelligence.<\/p>\r\n\r\n<p>The enemy is moving its units around according to a fixed scheme: for each fort a fraction of the units is moved to other forts in each time unit (the time of the flight is negligible).<\/p>\r\n\r\n<p>Now the government has fixed a time when to attack. Your order is to compute the weak points. But as the enemy&rsquo;s galaxy is far, far away it takes one time unit to fly there. Furthermore, we are also certain that the MdI will recognize our target and immediately start all ships which can reach our attacking point (via one link, regardless of its direction). The spy informed you that these strengths are only statistical values, i.e. some sort of indicator as float.<\/p>\r\n","input":"<p>The first line of the input contains the number of test cases (1 &le; T &le; 10). Each test case starts with one line containing three integers stating the number of enemy forts N (1 &le; N &le; 100), the number of links l (0 &le; l &le; (N - 1)<sup>2<\/sup>) and the time from now when to attack t (0 &le; t &le; 5000). The second line contains N doubles u<sub>i<\/sub> (0 &le; u<sub>i<\/sub> &le; 1000) specifying the strength of the stationed troops at each fort followed by l lines containing the links. Each link is described by two integers s<sub>j<\/sub> (0 &le; s<sub>j<\/sub> &lt; N), t<sub>j<\/sub> (0 &le; t<sub>j<\/sub> &lt; N) describing the source and the target of the link and one double p<sub>j<\/sub> (0 &lt; p<sub>j<\/sub> &le; 1), the fraction of units transferred from s<sub>j<\/sub> to t<sub>j<\/sub> in each time unit.<\/p>\r\n","output":"<p>Print the lowest indicator of the enemy galaxy with an absolute or relative error less than 10<sup>-6<\/sup>.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/timing1(1).png\" style=\"height:130px; width:530px\" \/><\/p>\r\n\r\n<p><strong>Figure 3<\/strong> &ndash; The statistical strengths of the first sample before and after the \ufb01rst time step.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/timing2.png\" style=\"height:133px; width:496px\" \/><\/p>\r\n\r\n<p><strong>Figure 4<\/strong> &ndash; Strength of the forces to face at each fort. Note that links are used in both directions.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]