Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in C (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

typedef struct A* ITEM;

typedef struct qnode qnode;

struct qnode{
    ITEM item;
    qnode *prev, *next;
};

typedef struct {
    qnode *head, *tail;
    int size;
}Queue;

Queue* qInit();
qnode* qNew(ITEM);
void   add(Queue*, ITEM);
ITEM   poll(Queue*);
ITEM   qElementAt(Queue*, int);

#include <stdlib.h>

Queue *qInit() {
    Queue *q = NULL;
    q = malloc(sizeof(Queue));
    q->head = NULL;
    q->tail = NULL;
    q->size = 0;
    return q;
}

qnode *qNew(ITEM item) {
    qnode *node = NULL;
    node = malloc(sizeof(qnode));
    node->item = item;
    node->prev = NULL;
    node->next = NULL;
    return node;
}

void add(Queue *q, ITEM item) {
    qnode *node = qNew(item);
    if (q->size == 0) {
        q->head = node;
        q->tail = node;
    }
    else {
        q->tail->next = node;
        node->prev = q->tail;
        q->tail = node;
    }
    q->size++;
}

ITEM poll(Queue *q) {
    qnode *node = q->head;
    if (q->size == 1) {
        q->head = NULL;
        q->tail = NULL;
    }
    else {
        q->head = node->next;
        q->head->prev = NULL;
    }
    q->size--;
    return node->item;
}

ITEM qElementAt(Queue *q, int n) {
    if (n > q->size || n < 0) exit(-1);
    int i;
    qnode *crawl = q->head;
    for(i = 0; i < n; i++) crawl = crawl->next;
    return crawl->item;
}

struct A {
    long long current;
    long long time;
};


struct A *newA(long long current, long long time) {
    struct A *a;
    a = malloc(sizeof(struct A));
    a->current = current;
    a->time = time;
    return a;
}

int main(void) {
    long long X;
    struct A *a;
    scanf("%lld", &X);
    Queue *queue = qInit();
    add(queue, newA(0, 0));
    while (queue->size) {
        a = poll(queue);
//        printf("%lld, %lld\n", a->current, a->time);
        if (a->current == X) break;
        add(queue, newA(a->current, a->time + 1));
        add(queue, newA(a->current + a->time + 1, a->time + 1));
        if (a->current - a->time - 1 >= -X) add(queue, newA(a->current - a->time - 1, a->time + 1));
    }
    printf("%lld\n", a->time);
    return 0;
}