Coins And Triangle
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Read problems statements in Mandarin Chinese , Russian and Vietnamese as well.
Chef belongs to a very rich family which owns many gold mines. Today, he brought N gold coins and decided to form a triangle using these coins. Isn't it strange?
Chef has a unusual way of forming a triangle using gold coins, which is described as follows:
- He puts 1 coin in the 1st row.
- then puts 2 coins in the 2nd row.
- then puts 3 coins in the 3rd row.
- and so on as shown in the given figure.
Chef is interested in forming a triangle with maximum possible height using at most N coins. Can you tell him the maximum possible height of the triangle?
The first line of input contains a single integer T denoting the number of test cases.
The first and the only line of each test case contains an integer N denoting the number of gold coins Chef has.
For each test case, output a single line containing an integer corresponding to the maximum possible height of the triangle that Chef can get.
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 109
- Subtask 1 (48 points) : 1 ≤ N ≤ 105
- Subtask 2 (52 points) : 1 ≤ N ≤ 109
Input 3 3 5 7 Output 2 2 3
- Test 1: Chef can't form a triangle with height > 2 as it requires atleast 6 gold coins.
- Test 2: Chef can't form a triangle with height > 2 as it requires atleast 6 gold coins.
- Test 3: Chef can't form a triangle with height > 3 as it requires atleast 10 gold coins.
|Tags||binary-search, cakewalk, implementation, ltime35, ma5termind, mathematics, sqrt|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, CLOJ, FS|
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