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Fighting 2019!

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Ivan wants to make a necklace as a present to his beloved girl. A necklace is a cyclic sequence of beads of different colors. Ivan says that necklace is beautiful relative to the cut point between two adjacent beads, if the chain of beads remaining after this cut is a palindrome (reads the same forward and backward).

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Yaroslav has n points that lie on the Ox axis. The coordinate of the first point is x_1, the coordinate of the second point is x_2, ..., the coordinate of the n-th point is — x_n. Now Yaroslav wants to execute m queries, each of them is of one of the two following types:

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In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation

F_1 = 1; F_2 = 1; F_n = F_{n - 1} + F_{n - 2} (n > 2)

DZY loves Fibonacci numbers very much. Today DZY gives you an array consisting of n integers: a_1, a_2, \dots, a_n. Moreover, there are m queries, each query has one of the two types:

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留一点点的距离,让我与世界分离
曾经困扰我的恐惧,消失在我回忆
夜里冰冷的空气,我终于能呼吸
我留下自己的过去,抹掉眼泪的痕迹

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