Jumping Worm

A forest has $N$ trees standing in a row at positions 1 through $N$. Tree $i$ has height $h_i$. The worm is at the base of tree 1, at height 0, and it wants to reach the top of tree $N$, at height $h_N$.

The worm can make one of two moves.

1. Climb. On tree $i$ it climbs $u_i$ units up. It can never go above the tree, so from height $y$ the new height is $\min(y + u_i, h_i)$.
2. Jump. It jumps to an adjacent tree, tree $i-1$ or tree $i+1$. It crosses at the same height, but if the top of the adjacent tree is lower than its current height, it lands on the top of that lower tree. Jumping to tree $j$ from height $y$ leaves the worm at height $\min(y, h_j)$.

Each move takes exactly 1 second, even when the top or the base of a tree cuts the move short.

After a move the worm must rest for 1 second, and while it rests gravity drags it down by $d_i$ units on tree $i$. It never goes below height 0. There is one exception. If a move leaves the worm on the top of the tree it is standing on, it does not rest and moves again right away.

The trip ends the moment the worm reaches the top of tree $N$.

Given the number of trees and every $h_i$, $u_i$ and $d_i$, find the shortest travel time in seconds from the base of tree 1 to the top of tree $N$.

Consider 8 trees whose heights from left to right are 5, 5, 3, 3, 3, 4, 5, 5, where every $u_i$ is 3 and every $d_i$ is 2. Three climbs from the base of tree 1 with two rests in between put the worm on the top of tree 1 at second 5. It is on a top, so it does not rest, and from second 6 through second 9 it jumps to trees 2, 3, 4 and 5, landing on the top of each one and resting none of those times. At second 10 it jumps to tree 6 and stands at height 3, but the top of tree 6 is 4, so it rests at second 11 and slides to height 1. It climbs at second 12 to the top of tree 6, jumps at second 13 to tree 7 and stands at height 4, rests at second 14 down to height 2, climbs at second 15 to the top of tree 7 at height 5, and jumps at second 16 to tree 8, where height 5 is the top and the trip ends. That route takes 16 seconds, and it is not the fastest one. Jumping along the bases of all eight trees and climbing only the last one takes 19 seconds: a jump made below a top is always followed by a rest, and at height 0 the worm cannot slide any lower.

The first line has the number of test cases $K$. ($1 \le K \le 10$)

Each test case has four lines.

1. The first line has the number of trees $N$. ($1 \le N \le 1000$)
2. The second line has $h_1, h_2, \dots, h_N$, where $h_i$ is the height of tree $i$. ($1 \le h_i \le 1000$)
3. The third line has $u_1, u_2, \dots, u_N$, where $u_i$ is the climb rate of tree $i$. ($1 \le u_i \le 1000$)
4. The fourth line has $d_1, d_2, \dots, d_N$, where $d_i$ is the fall rate of tree $i$. ($0 \le d_i \le 1000$)

For each test case print one line with the shortest travel time in seconds. If the worm cannot reach the top of tree $N$, print NEVER in capital letters.