In some poker games, such as Texas Hold'em, dealing cards is a delicate process. A professional dealer is generally called a croupier. Before dealing, the croupier must "burn" a card. Burning a card means moving the card currently at the top of the deck to the bottom of the deck; this is used to prevent players from guessing cards and influencing the game.

Suppose that at the beginning, the croupier takes out a new deck of cards. This deck has $N$ distinct cards, numbered from $1$ to $N$ in order. Since it is a new deck, the cards are arranged in order, starting from the top of the deck as $1, 2, \dots, N$, with card $N$ at the bottom. To deal all the cards, the croupier performs $N$ dealing operations. Before the $i$-th deal, the croupier performs $R_i$ consecutive burn operations, where $R_i$ is given by the input. What is the order in which the player receives the cards?

For example, suppose $N=4$. Initially, the order of cards in the deck is $\{1, 2, 3, 4\}$.

Suppose $R_1 = 2$. The croupier should burn two cards, moving $1$ and $2$ to the bottom of the deck, and then deal $3$ to the player. The current order of cards in the deck is $\{4, 1, 2\}$.

Suppose $R_2 = 0$. The croupier does not need to burn any cards and deals $4$ directly to the player. The current order of cards in the deck is $\{1, 2\}$.

Suppose $R_3 = 3$. The croupier burns $1, 2, 1$ in sequence, and then deals $2$ to the player. The deck now has only one card left, $1$.

Suppose $R_4 = 2$. The croupier repeats burning $1$ twice, and then deals $1$ to the player, because $1$ is the only card left in the deck.

Input

The first line contains an integer $N$, representing the number of cards.

From the second line to the $N+1$-th line, the $(i+1)$-th line contains an integer $R_i$, where $0 \le R_i < N$.

Output

From the first line to the $N$-th line: the $i$-th line contains a single integer, representing the number of the $i$-th card received by the player.

Examples

Input 1

4
2
0
3
2

Output 1

3
4
2
1

Constraints

The sizes of the ten test cases are as follows:

Figure 1. Example of burn operation R1 = 2