Codeforces Round 172 (Div. 2)
A. Word Capitalization
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Capitalization is writing a word with its first letter as a capital letter. Your task is to capitalize the given word.

Note, that during capitalization all the letters except the first one remains unchanged.

Input

A single line contains a non-empty word. This word consists of lowercase and uppercase English letters. The length of the word will not exceed 103.

Output

Output the given word after capitalization.

Examples
Input
ApPLe
Output
ApPLe
Input
konjac
Output
Konjac
B. Nearest Fraction
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction whose denominator is no more than n.

Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value is as minimal as possible.

If there are multiple "nearest" fractions, choose the one with the minimum denominator. If there are multiple "nearest" fractions with the minimum denominator, choose the one with the minimum numerator.

Input

A single line contains three integers x, y, n (1 ≤ x, y, n ≤ 105).

Output

Print the required fraction in the format "a/b" (without quotes).

Examples
Input
3 7 6
Output
2/5
Input
7 2 4
Output
7/2
C. Rectangle Puzzle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the Ox axis, equals w, the length of the side that is parallel to the Oy axis, equals h. The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle α.

Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

Input

The first line contains three integers w, h, α (1 ≤ w, h ≤ 106; 0 ≤ α ≤ 180). Angle α is given in degrees.

Output

In a single line print a real number — the area of the region which belongs to both given rectangles.

The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples
Input
1 1 45
Output
0.828427125
Input
6 4 30
Output
19.668384925
Note

The second sample has been drawn on the picture above.

D. Maximum Xor Secondary
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Bike loves looking for the second maximum element in the sequence. The second maximum element in the sequence of distinct numbers x1, x2, ..., xk (k > 1) is such maximum element xj, that the following inequality holds: .

The lucky number of the sequence of distinct positive integers x1, x2, ..., xk (k > 1) is the number that is equal to the bitwise excluding OR of the maximum element of the sequence and the second maximum element of the sequence.

You've got a sequence of distinct positive integers s1, s2, ..., sn (n > 1). Let's denote sequence sl, sl + 1, ..., sr as s[l..r] (1 ≤ l < r ≤ n). Your task is to find the maximum number among all lucky numbers of sequences s[l..r].

Note that as all numbers in sequence s are distinct, all the given definitions make sence.

Input

The first line contains integer n (1 < n ≤ 105). The second line contains n distinct integers s1, s2, ..., sn (1 ≤ si ≤ 109).

Output

Print a single integer — the maximum lucky number among all lucky numbers of sequences s[l..r].

Examples
Input
5
5 2 1 4 3
Output
7
Input
5
9 8 3 5 7
Output
15
Note

For the first sample you can choose s[4..5] = {4, 3} and its lucky number is (4 xor 3) = 7. You can also choose s[1..2].

For the second sample you must choose s[2..5] = {8, 3, 5, 7}.

E. Game on Tree
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Momiji has got a rooted tree, consisting of n nodes. The tree nodes are numbered by integers from 1 to n. The root has number 1. Momiji decided to play a game on this tree.

The game consists of several steps. On each step, Momiji chooses one of the remaining tree nodes (let's denote it by v) and removes all the subtree nodes with the root in node v from the tree. Node v gets deleted as well. The game finishes when the tree has no nodes left. In other words, the game finishes after the step that chooses the node number 1.

Each time Momiji chooses a new node uniformly among all the remaining nodes. Your task is to find the expectation of the number of steps in the described game.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of nodes in the tree. The next n - 1 lines contain the tree edges. The i-th line contains integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the numbers of the nodes that are connected by the i-th edge.

It is guaranteed that the given graph is a tree.

Output

Print a single real number — the expectation of the number of steps in the described game.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples
Input
2
1 2
Output
1.50000000000000000000
Input
3
1 2
1 3
Output
2.00000000000000000000
Note

In the first sample, there are two cases. One is directly remove the root and another is remove the root after one step. Thus the expected steps are:

1 × (1 / 2) + 2 × (1 / 2) = 1.5

In the second sample, things get more complex. There are two cases that reduce to the first sample, and one case cleaned at once. Thus the expected steps are:

1 × (1 / 3) + (1 + 1.5) × (2 / 3) = (1 / 3) + (5 / 3) = 2