Two treasure hunters each sketched a branching trail map starting from a single landmark: from any landmark at most two trails continue onward, called the left trail and the right trail, and every landmark records an amount of gold buried there. The hunters want to merge their maps into one: at any position in the branching layout where both maps have a landmark, the merged landmark holds the sum of both gold amounts; at any position where only one map has a landmark, the merged map simply keeps that entire landmark and everything reachable further down its trails, untouched; positions with no landmark in either map stay empty. Given both maps, output the merged map.

Input format

• Line 1: the first map, written breadth-first (the starting landmark first, then each level left to right) as space-separated tokens, where each token is either an integer gold amount or the literal null marking a position with no landmark. A landmark's left-trail and right-trail tokens follow later in the same sequence, in the order their landmarks were reached; a null position contributes no further tokens of its own. If the sequence runs out of tokens before a landmark's trail tokens appear, treat those trails as absent. A map with no landmarks at all is written as the single token null.
• Line 2: the second map, written in the same style.

Output format

• A single line: the merged map, written in the same breadth-first style as the input (trailing null tokens at the end of the line are, and should be, omitted). Print null if the merged map has no landmarks.

Constraints

• Each map has between 0 and 1000 landmarks.
• -1000 <= gold amount <= 1000.

1 3 2 5
2 1 3 null 4 null 7

3 4 5 5 4 null 7

null
5 2 8

5 2 8