CF767C.Garland

Once at New Year Dima had a dream in which he was presented a fairy garland. A garland is a set of lamps, some pairs of which are connected by wires. Dima remembered that each two lamps in the garland were connected directly or indirectly via some wires. Furthermore, the number of wires was exactly one less than the number of lamps.

There was something unusual about the garland. Each lamp had its own brightness which depended on the temperature of the lamp. Temperatures could be positive, negative or zero. Dima has two friends, so he decided to share the garland with them. He wants to cut two different wires so that the garland breaks up into three parts. Each part of the garland should shine equally, i. e. the sums of lamps' temperatures should be equal in each of the parts. Of course, each of the parts should be non-empty, i. e. each part should contain at least one lamp.

Help Dima to find a suitable way to cut the garland, or determine that this is impossible.

While examining the garland, Dima lifted it up holding by one of the lamps. Thus, each of the lamps, except the one he is holding by, is now hanging on some wire. So, you should print two lamp ids as the answer which denote that Dima should cut the wires these lamps are hanging on. Of course, the lamp Dima is holding the garland by can't be included in the answer.

新年时，迪马曾做过一个梦，在梦中他收到了一条仙女花环。花环由若干盏灯组成，其中某些灯对之间通过导线相连。迪马记得，花环中任意两盏灯之间都直接或间接地通过若干导线连通；此外，导线的数量恰好比灯的数量少一。

这条花环有些特别：每盏灯都有其自身的亮度，该亮度取决于灯的温度。温度可以是正数、负数或零。迪马有两个朋友，因此他决定将花环与他们分享。他想剪断两条不同的导线，使得花环被分割成三个部分，且每个部分的总亮度（即各灯温度之和）均相等。当然，每个部分都必须非空，即每个部分至少包含一盏灯。

请帮助迪马找出一种合适的剪断方式，或者判定这是不可能的。

在检查花环时，迪马用手拎起其中一盏灯，于是除他所持的那盏灯外，其余每盏灯都悬挂在某根导线上。因此，你的答案应输出两个灯的编号，表示迪马应剪断这两盏灯所悬挂的导线。当然，迪马所持的那盏灯不能出现在答案中。

The first line contains single integer n (3 ≤ n ≤ 106) — the number of lamps in the garland.

Then n lines follow. The i-th of them contain the information about the i-th lamp: the number lamp a__i, it is hanging on (and 0, if is there is no such lamp), and its temperature t__i ( - 100 ≤ t__i ≤ 100). The lamps are numbered from 1 to n.

第一行包含一个整数 $n$（$3 \leq n \leq 10^6$）——彩灯串中彩灯的数量。

接下来有 $n$ 行。其中第 $i$ 行包含关于第 $i$ 盏彩灯的信息：该彩灯所悬挂的彩灯编号 $a_i$（若无悬挂彩灯，则为 $0$），以及其温度 $t_i$（$-100 \leq t_i \leq 100$）。彩灯编号从 $1$ 到 $n$。

If there is no solution, print -1.

Otherwise print two integers — the indexes of the lamps which mean Dima should cut the wires they are hanging on. If there are multiple answers, print any of them.

如果无解，输出 -1。

否则输出两个整数——即 Dima 应当切断其悬挂电线的两盏灯的编号。若存在多个答案，输出任意一个即可。

The garland and cuts scheme for the first example:

第一个示例的花环与切割方案：