Jewelry Box

There are N jewelry shops numbered 1 to N.

Shop i (1 \leq i \leq N) sells K_i kinds of jewels. The j-th of these jewels (1 \leq j \leq K_i) has a size and price of S_{i,j} and P_{i,j}, respectively, and the shop has C_{i,j} jewels of this kind in stock.

A jewelry box is said to be good if it satisfies all of the following conditions:

• For each of the jewelry shops, the box contains one jewel purchased there.
• All of the following M restrictions are met.
• Restriction i (1 \leq i \leq M): (The size of the jewel purchased at Shop V_i)\leq (The size of the jewel purchased at Shop U_i)+W_i

Answer Q questions. In the i-th question, given an integer A_i, find the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes. If it is impossible to make A_i good jewelry boxes, report that fact.

Constraints

• 1 \leq N \leq 30
• 1 \leq K_i \leq 30
• 1 \leq S_{i,j} \leq 10^9
• 1 \leq P_{i,j} \leq 30
• 1 \leq C_{i,j} \leq 10^{12}
• 0 \leq M \leq 50
• 1 \leq U_i,V_i \leq N
• U_i \neq V_i
• 0 \leq W_i \leq 10^9
• 1 \leq Q \leq 10^5
• 1 \leq A_i \leq 3 \times 10^{13}
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Description of Shop 1 Description of Shop 2 \vdots Description of Shop N M U_1 V_1 W_1 U_2 V_2 W_2 \vdots U_M V_M W_M Q A_1 A_2 \vdots A_Q

The description of Shop i (1 \leq i \leq N) is in the following format:

K_i S_{i,1} P_{i,1} C_{i,1} S_{i,2} P_{i,2} C_{i,2} \vdots S_{i,K_i} P_{i,K_i} C_{i,K_i}

Output

Print Q lines. The i-th line should contain the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes, or -1 if it is impossible to make them.

Examples

Input

3 2 1 10 1 3 1 1 3 1 10 1 2 1 1 3 10 1 2 1 1 1 3 10 1 2 1 2 0 2 3 0 3 1 2 3

Output

3 42 -1

Input

5 5 86849520 30 272477201869 968023357 28 539131386006 478355090 8 194500792721 298572419 6 894877901270 203794105 25 594579473837 5 730211794 22 225797976416 842538552 9 420531931830 871332982 26 81253086754 553846923 29 89734736118 731788040 13 241088716205 5 903534485 22 140045153776 187101906 8 145639722124 513502442 9 227445343895 499446330 6 719254728400 564106748 20 333423097859 5 332809289 8 640911722470 969492694 21 937931959818 207959501 11 217019915462 726936503 12 382527525674 887971218 17 552919286358 5 444983655 13 487875689585 855863581 6 625608576077 885012925 10 105520979776 980933856 1 711474069172 653022356 19 977887412815 10 1 2 231274893 2 3 829836076 3 4 745221482 4 5 935448462 5 1 819308546 3 5 815839350 5 3 513188748 3 1 968283437 2 3 202352515 4 3 292999238 10 510266667947 252899314976 510266667948 374155726828 628866122125 628866122123 1 628866122124 510266667949 30000000000000

Output

26533866733244 13150764378752 26533866733296 19456097795056 -1 33175436167096 52 33175436167152 26533866733352 -1

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N Description of Shop 1 Description of Shop 2 \vdots Description of Shop N M U_1 V_1 W_1 U_2 V_2 W_2 \vdots U_M V_M W_M Q A_1 A_2 \vdots A_Q

The description of Shop i (1 \leq i \leq N) is in the following format:

K_i S_{i,1} P_{i,1} C_{i,1} S_{i,2} P_{i,2} C_{i,2} \vdots S_{i,K_i} P_{i,K_i} C_{i,K_i}

outputFormat

Output

Print Q lines. The i-th line should contain the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes, or -1 if it is impossible to make them.

Examples

Input

3 2 1 10 1 3 1 1 3 1 10 1 2 1 1 3 10 1 2 1 1 1 3 10 1 2 1 2 0 2 3 0 3 1 2 3

Output

3 42 -1

Input

5 5 86849520 30 272477201869 968023357 28 539131386006 478355090 8 194500792721 298572419 6 894877901270 203794105 25 594579473837 5 730211794 22 225797976416 842538552 9 420531931830 871332982 26 81253086754 553846923 29 89734736118 731788040 13 241088716205 5 903534485 22 140045153776 187101906 8 145639722124 513502442 9 227445343895 499446330 6 719254728400 564106748 20 333423097859 5 332809289 8 640911722470 969492694 21 937931959818 207959501 11 217019915462 726936503 12 382527525674 887971218 17 552919286358 5 444983655 13 487875689585 855863581 6 625608576077 885012925 10 105520979776 980933856 1 711474069172 653022356 19 977887412815 10 1 2 231274893 2 3 829836076 3 4 745221482 4 5 935448462 5 1 819308546 3 5 815839350 5 3 513188748 3 1 968283437 2 3 202352515 4 3 292999238 10 510266667947 252899314976 510266667948 374155726828 628866122125 628866122123 1 628866122124 510266667949 30000000000000

Output

26533866733244 13150764378752 26533866733296 19456097795056 -1 33175436167096 52 33175436167152 26533866733352 -1

样例

5
5
86849520 30 272477201869
968023357 28 539131386006
478355090 8 194500792721
298572419 6 894877901270
203794105 25 594579473837
5
730211794 22 225797976416
842538552 9 420531931830
871332982 26 81253086754
553846923 29 89734736118
731788040 13 241088716205
5
903534485 22 140045153776
187101906 8 145639722124
513502442 9 227445343895
499446330 6 719254728400
564106748 20 333423097859
5
332809289 8 640911722470
969492694 21 937931959818
207959501 11 217019915462
726936503 12 382527525674
887971218 17 552919286358
5
444983655 13 487875689585
855863581 6 625608576077
885012925 10 105520979776
980933856 1 711474069172
653022356 19 977887412815
10
1 2 231274893
2 3 829836076
3 4 745221482
4 5 935448462
5 1 819308546
3 5 815839350
5 3 513188748
3 1 968283437
2 3 202352515
4 3 292999238
10
510266667947
252899314976
510266667948
374155726828
628866122125
628866122123
1
628866122124
510266667949
30000000000000

26533866733244
13150764378752
26533866733296
19456097795056
-1
33175436167096
52
33175436167152
26533866733352
-1

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