codeforce1029B B. Creating the Contest(简单dp，简单版单调栈)

codeforce1029B B. Creating the Contest(简单dp，简单版单调栈)

B. Creating the Contest

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a problemset consisting of $\mathrm{nn problems.\; The\; difficulty\; of\; the ii-th\; problem\; is aiai.\; It\; is\; guaranteed\; that\; all\; difficulties\; are\; distinct\; and\; are\; given\; in\; the\; increasing\; order.}$

You have to assemble the contest which consists of some problems of the given problemset. In other words, the contest you have to assemble should be a subset of problems (not necessary consecutive) of the given problemset. There is only one condition that should be satisfied: for each problem but the hardest one (the problem with the maximum difficulty) there should be a problem with the difficulty greater than the difficulty of this problem but not greater than twice the difficulty of this problem. In other words, let ${\mathrm{ai1,ai2,\dots ,aipai1,ai2,\dots ,aip be\; the\; difficulties\; of\; the\; selected\; problems\; in\; increasing\; order.\; Then\; for\; each jj from 11 to p-1p-1 aij+1\le aij\cdot 2aij+1\le aij\cdot 2 should\; hold. It\; means\; that\; the\; contest\; consisting\; of\; only\; one\; problem\; is\; always\; valid.}}^{}$

Among all contests satisfying the condition above you have to assemble one with the maximum number of problems. Your task is to find this number of problems.

Input

The first line of the input contains one integer $\mathrm{nn (1\le n\le 2\cdot 1051\le n\le 2\cdot 105)\; —\; the\; number\; of\; problems\; in\; the\; problemset.}$

The second line of the input contains $\mathrm{nn integers a1,a2,\dots ,ana1,a2,\dots ,an (1\le ai\le 1091\le ai\le 109)\; —\; difficulties\; of\; the\; problems. It\; is\; guaranteed\; that\; difficulties\; of\; the\; problems\; are\; distinct\; and\; are\; given\; in\; the\; increasing\; order.}$

Output

Print a single integer — maximum number of problems in the contest satisfying the condition in the problem statement.

Examples

input

Copy

10
1 2 5 6 7 10 21 23 24 49

output

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4

input

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5
2 10 50 110 250

output

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1

input

Copy

6
4 7 12 100 150 199

output

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3

Note

Description of the first example: there are $\mathrm{1010 valid\; contests\; consisting\; of 11 problem, 1010 valid\; contests\; consisting\; of 22 problems\; ([1,2],[5,6],[5,7],[5,10],[6,7],[6,10],[7,10],[21,23],[21,24],[23,24][1,2],[5,6],[5,7],[5,10],[6,7],[6,10],[7,10],[21,23],[21,24],[23,24]), 55 valid\; contests\; consisting\; of 33 problems\; ([5,6,7],[5,6,10],[5,7,10],[6,7,10],[21,23,24][5,6,7],[5,6,10],[5,7,10],[6,7,10],[21,23,24])\; and\; a\; single\; valid\; contest\; consisting\; of 44 problems\; (}$